THE VALUE OF CREDITOR GOVERNANCE: DEBT RENEGOTIATIONS IN AND OUTSIDE DISTRESS

MARC ARNOLD RAMONA WESTERMANN WORKING PAPERS ON FINANCE NO. 2015/14 SWISS INSTITUTE OF BANKING AND FINANCE (S/BF – HSG)

JULY 2015 THIS VERSION: JULY 2016

The Value of Creditor Governance:

Debt Renegotiations In and Outside Distress∗

Marc Arnold† and Ramona Westermann‡

ABSTRACT

This paper analyzes a structural model of a levered firm that can renegotiate

debt outside and in distress. The firm renegotiates outside distress to waive its

financing covenant when raising investment funds and renegotiates in distress to

avoid bankruptcy costs. Incorporating the ability to renegotiate both outside and

in distress is crucial to explaining timing patterns of debt renegotiations. Capturing

realistic incentives and timing patterns of renegotiations allows us to quantify the

value of creditor governance. We explain a rich set of empirical facts in terms of

influence of renegotiable debt on security values and corporate policies.

JEL Classification Numbers: D92, E44, G12, G32, G33.

Keywords: Renegotiation, Debt Covenants, Corporate Investment, Capital Struc-

ture.

∗We are grateful to Jens Dick-Nielsen, Christian Riis Floor, Stefan Hirth, Kristian Miltersen, ErwanMorellec, Kjell Nyborg, Mads Stenbo Nielsen, Lasse Heje Pedersen, Remy Praz, and Suresh Sundaresanfor valuable comments and suggestions. This paper has also benefited from comments of seminar andconference participants at Aarhus University, Copenhagen Business School, the University of SouthernDenmark, the University of St. Gallen, and the Young Scholars Nordic Finance conference. RamonaWestermann gratefully acknowledges support from the European Research Council (ERC grant no.312417) and the FRIC Center for Financial Frictions (grant no. DNRF102). A previous version ofthis paper circulated under the title “Debt Covenant Renegotiation and Investment”.†University of St. Gallen, Rosenbergstrasse 52, 9000 St. Gallen, Switzerland. email:

marc.arnold@unisg.ch‡Copenhagen Business School, Solbjerg Plads 3, 2000 Frederiksberg, Denmark. email: rw.fi@cbs.dk

1. Introduction

The traditional governance approach presumes that managers and equity holders de-

termine firm policies and debt holders are passive unless a firm is in distress. Recent

empirical studies challenge this view with evidence that creditors influence corporate de-

cisions through debt renegotiations. Specifically, such renegotiations occur frequently, are

mostly not due to distress, and have a profound impact on corporate policies (Roberts

and Sufi, 2009b; Nini, Smith, and Sufi, 2012; Denis and Wang, 2014; Roberts, 2015). Yet,

the theoretical literature lacks a model that rationalizes the timing when debt renegotia-

tions occur. Capturing the timing patterns, however, is crucial to assess the quantitative

impact of creditors’ influence on firms.

This paper develops a model to quantify the impact of firms’ ability to renegotiate

debt. The novelty of this model is that firms can renegotiate their debt not only in

distress, but also outside distress when new funds are raised. We call this renegotiation

model the “R-model”. The R-model is based on a structural corporate finance framework

of a levered firm in the spirit of Mello and Parsons (1992). To incorporate cross sectional

differences in expected financing needs, we consider an investment opportunity as modeled

in Hackbarth and Mauer (2012). Following Fan and Sundaresan (2000), firms in distress

renegotiate debt with a debt-equity swap (distressed reorganization) to avoid bankruptcy

costs. We also allow firms to include a covenant that restricts subsequent debt financing

in the initial debt contract. Firms’ aspiration to raise new debt funds at investment leads

to debt renegotiation outside distress. Firms implement the covenant ex-ante because

renegotiation with the initial debt holders at investment disciplines the ex-post investment

and financing decisions. This mechanism to mitigate the agency costs of debt is consistent

with the recent empirical literature showing that non-distressed covenant renegotiation

constitutes an important governance channel through which debt holders influence firm

policies such as investment, operating, or financing decisions (e.g., Roberts, 2015).

The R-model provides several key implications for creditor governance. Specifically,

it explains the impact of renegotiable debt on (1) timing patterns, (2) credit spreads, (3)

firm value, and (4) corporate policies. First, we show that incorporating renegotiation

both outside and in distress is crucial to rationalize the empirically observed timing

patterns of renegotiation. Second, the R-model explains the impact of debt renegotiation

on credit spreads. It is consistent with the average empirical credit spreads and improves

the ability of structural models to match the cross section of observed debt prices. Third,

1

having a model with realistic motives and timing patterns of renegotiations allows us

to quantify the impact of the ability to renegotiate debt on firms. We find that debt

renegotiation constitutes an economically important governance channel that increases

baseline firm value by 3.8%. Fourth, the R-model explains empirical facts and generates

novel predictions on covenant structures and corporate financial policies. We proceed by

explaining each of these key findings in more detail.

First, we investigate to what extent the R-model rationalizes the timing patterns of

debt renegotiations. As empirical benchmark, we use the sample of private credit agree-

ments in Nini, Smith, and Sufi (2009), for which Denis and Wang (2014) and Roberts and

Sufi (2009b) report stylized facts of debt renegotiation patterns. We generate simulated

samples of model-implied firms that are structurally similar to this real firms sample. In

addition to the R-model, we use a model that considers only distressed reorganization;

we label this model the “FSI-model.” Finally, we compare timing patterns of debt rene-

gotiations in the simulated samples to those in the real firms sample. Empirically, the

average time elapsed to a renegotiation is around 59% of the initially stated maturity.

The R-model closely reflects this statistic by implying a duration of 60.6%. Conversely,

the FSI-model predicts a duration of 96.2%, which is well beyond the empirical counter-

part. We also show that by including non-distressed renegotiation, we can improve the

matching of many additional empirical renegotiation timing patterns.

Second, we use the R-model to explain how renegotiable debt affects credit spreads

and debt control premiums. The R-model reflects the average observed credit spreads.

It also explains the empirical impact reported in Davydenko and Strebulaev (2007) of

the ability to renegotiate debt, bargaining power, and liquidation costs on credit spreads.

Additionally, the R-model generates a debt control premium, which is discovered in the

recent empirical work of Feldhutter, Hotchkiss, and Karakas (forthcoming). While ex-

isting structural models are quite successful in replicating the average observed credit

spreads (Chen, 2010; Bhamra, Kuehn, and Strebulaev, 2010), they still struggle to ex-

plain the cross-firm variation in credit spreads (Eom, Helwege, and Huang, 2004; Zhang,

Zhou, and Zhu, 2009). We show that incorporating debt renegotiation provides a crucial

step towards quantitatively rationalizing the cross section of observed credit spreads. The

improvement, however, arises only when we consider that debt renegotiations can occur

both in distress and outside distress. Our debt pricing results are also of interest for

practitioners. They imply that covenant structure, bargaining power, and renegotiation

2

frictions are quantitatively important to estimate the credit spread of a firm, in addition

to the parameters traditionally associated with default risk.

Third, we investigate the quantitative impact of the ability to renegotiate debt on firm

value. We start by quantifying the benefit of installing a renegotiable financing covenant.

This benefit arises from a mitigation in the agency cost of debt. Specifically, the issuance

of new debt to finance the investment cost dilutes the initial debt claim and, hence,

transfers wealth from initial debt to equity holders. Therefore, firms without covenant

protection acting in the interest of equity holders expropriate initial debt holders through

overlevering at investment and overinvestment compared to policies that maximize firm

value (Hackbarth and Mauer, 2012). A covenant prohibiting the issuance of new debt

protects initial debt holders from this ex-post claim dilution. In case the covenant is

enforced, equity holders have to finance the investment cost by issuing additional equity.

To increase the value of their claim by the additional tax shield of new debt, equity

holders prefer to renegotiate the covenant with initial debt holders at investment. We

model this renegotiation as a bargaining game and solve for the Nash solution. This

solution allows us to assign different levels of bargaining power to the two parties. Equity

holders offer initial debt holders an increase in promised interest rate in exchange for

waiving the covenant. This offer reflects that debt holders can negotiate a change in debt

terms that improves the value of their claim in many real cases of non-distressed covenant

renegotiations (Kahan and Rock, 2009; Feldhutter, Hotchkiss, and Karakas, forthcoming).

The increase in promised interest rate and amount of new debt are determined as the Nash

bargaining solution. We show that this solution to the renegotiation game leads to the

firm value maximizing leverage at investment. Covenant renegotiation also mitigates the

overinvestment problem because equity holders do not expropriate initial debt holders

at investment by issuing too much new debt. Thus, the possibility of debt covenant

renegotiation outside distress reduces the agency costs of debt due to overleverage and

overinvestment.

Installing a renegotiable covenant also carries a cost. Without this covenant, firms

have a relatively strong incentive to avoid distressed reorganization because they lose

the opportunity to expropriate debt holders ex-post. With this covenant, firms cannot

expropriate debt holders at investment. Hence, they reorganize earlier. A higher ten-

dency to distressed reorganization, however, is costly owing to the lost tax shield. This

mechanism emphasizes the importance of modeling the dependence between distressed

and non-distressed amendments to investigate the impact of renegotiable debt on firms.

3

The benefit of a renegotiable covenant dominates its cost such that firm value in-

creases when incorporating a covenant. Non-distressed covenant renegotiation is crucial

to quantify the total value of the ability to renegotiate debt. Specifically, considering

solely distressed reorganization increases firm value by only 1.87%. Additionally incor-

porating covenant renegotiation more than doubles this increase, namely, to 3.76%. This

number shows that debt renegotiation is an economically crucial governance channel that

considerably increases firm value. We also find that the bargaining power of equity hold-

ers is more important for firm value with both distressed and non-distressed renegotiation

than when incorporating only distressed reorganization.

Fourth, and finally, we explore the predictions of the R-model on corporate financial

policies. The finding that a renegotiable covenant considerably increases firm value pro-

vides a rationale for the frequent use of financing covenants. Roberts and Sufi (2009a),

for example, show that almost 90% of credit agreements contain a restriction on the bor-

rower’s total debt. By analyzing the impact of firm parameter variation on the benefit and

cost of installing a financing covenant, we can derive cross sectional covenant predictions.

For instance, firms with stronger bargaining power of equity holders or higher default

cost should have a lower tendency to restrict additional debt issuance with covenants.

We also show that the ability to renegotiate outside distress increases the optimal market

leverage. Additionally, it reduces the sensitivity of market leverage to the value of the

investment opportunity. The latter finding suggests that the empirical finding of Billett,

King, and Mauer (2007) that financing covenant restrictions attenuate the negative im-

pact of growth opportunities on leverage for public bonds applies to renegotiable private

debt as well. Our analysis indicates that this pattern should be even more pronounced for

private debt than for public debt. With respect to the timing of investment, the R-model

implies that a financing covenant delays investment mainly because equity holders cannot

expropriate debt holders upon investment.

Our paper addresses different veins of the literature. Most importantly, we contribute

to recent empirical studies suggesting that covenants are primarily renegotiated not to

avoid default, but rather to allow creditors intervene in firm policies subject to conflicts

of interest (Dichev and Skinner, 2002; Chava and Roberts, 2008; Denis and Wang, 2014;

Bradley and Roberts, 2015). Roberts and Sufi (2009b), Wang (2013), and Roberts (2015)

support this argument by showing that most debt renegotiations have little to do with

corporate distress or default. Even covenant violations rarely lead to firm liquidation

or acceleration of a loan but rather entail renegotiation resulting in stronger contractual

4

restrictions (Smith, Jr. and Warner, 1979; Nini, Smith, and Sufi, 2009; Gopalakrishnan

and Parkash, 1995). This literature concludes that debt renegotiation constitutes a debt

governance channel for creditors. We include this debt governance aspect by showing that

the ability to renegotiate debt reduces both the agency cost of debt and the expected

default costs. By exploring a model capturing the empirical timing patterns of debt

renegotiations, we provide the first quantitative analysis of the impact of renegotiation

as a debt governance channel on firms. Our insights complement those of Gamba and

Triantis (2014) who investigate how non-renegotiable debt covenants mitigate investment

and financing distortions.

The existing theoretical literature features several models incorporating either dis-

tressed reorganization or non-distressed renegotiation. The main idea behind the dis-

tressed reorganization models in Giammarino (1989), Anderson and Sundaresan (1996),

Mella-Barral and Perraudin (1997), Mella-Barral (1999), Fan and Sundaresan (2000), and

Sundaresan and Wang (2007) is that equity holders can reduce contractual debt obliga-

tions due to costly bankruptcy threats when firm performance deteriorates. Models with

non-distressed renegotiation, to the best of our knowledge, consider only static discrete

time approaches. The motives for renegotiation in these studies are related to invest-

ment. Bergman and Callen (1991) show that when firm profit is low, equity holders can

credibly threaten debt holders to adapt a suboptimal investment policy that saps firm

value. This threat allows them to renegotiate debt to their advantage. In Berlin and

Mester (1992), the firm manager has an incentive to underinvest in safe activities and

overinvest in growth activities. Covenants oblige to a minimum required investment in

safe activities. The value of the option to renegotiate stems from the ability to invest less

in safe activities and, consequently, more in growth activities when all parties realize that

an unfavorable outcome is unlikely. Gorton and Kahn (2000) examine the moral hazard

problem between the borrower and lender to analyze the design, pricing, and renego-

tiation of loan contracts. The borrower can undertake a costly, risk-increasing action

(asset substitution), whereas the lender can demand collateral upon the arrival of bad

news. The role of the initial debt contract is to impact the bargaining in the subsequent

contract renegotiation. As in the R-model, lenders extract some surplus from equity

holders’ investment decision by increasing the loan interest rates. Dessein (2005) argues

that good borrowers are willing to shift formal control rights over investment to the less

informed investor because they want to signal congruent preferences. Bad borrowers find

such concessions too costly. Garleanu and Zwiebel (2009) show that since the borrower

5

is better informed about the potential of future wealth transfer, lenders receive strong

ex-ante decision rights. When information is revealed, renegotiation occurs to transfer

some control rights back to the borrower.

We contribute to this theoretical literature in three ways. First, we show that one

needs to incorporate distressed and non-distressed renegotiation simultaneously to ex-

plain empirically observed renegotiation timing patterns. Second, we emphasize that

considering distressed and non-distressed renegotiations in isolation neglects the inherent

link between them. In particular, the anticipated outcome of non-distressed renegotiation

is a main driver of the distressed reorganization risk. Third, we provide a model captur-

ing the empirically observed motives and timing patterns of debt amendments, thereby

allowing us to quantify the impact of the ability to renegotiate debt and of bargaining

power on the value of corporate securities and firm policies.

Our paper also complements existing quantitative studies on the pricing of debt (Fan

and Sundaresan, 2000; Huang and Huang, 2012; Hackbarth, Miao, and Morellec, 2006;

Almeida and Philippon, 2007; Chen, Collin-Dufresne, and Goldstein, 2009; Bhamra,

Kuehn, and Strebulaev, 2010; Chen, 2010; Arnold, Wagner, and Westermann, 2013).

We show that the R-model explains the quantitative impact of debt renegotiation and

bargaining power on credit spreads. We, thereby, contribute to the literature by rational-

izing that not simply leverage, but also debt structure and debt ownership are important

to explain observed debt prices (Datta, Datta-Iskandar, and Patel, 1999; Davydenko and

Strebulaev, 2007; Lin, Ma, Malatesta, and Xuan, 2011; He and Xiong, 2012). Addition-

ally, we address the notion that debt prices reflect the surplus extracted by lenders, as

formalized by Rajan (1992) in a discrete time model. The corresponding control pre-

mium has recently been examined in the empirical bond pricing literature (Feldhutter,

Hotchkiss, and Karakas, forthcoming). To the best of our knowledge, we are the first to

assess the control premium quantitatively in a debt pricing model.

Finally, we speak to the literature on the impact of financing frictions on investment

(Whited, 1992; Hennessy, 2004; Childs, Mauer, and Ott, 2005; Chava and Roberts, 2008;

Hackbarth and Mauer, 2012). By modeling debt covenant renegotiation as a specific

channel through which financing frictions affect investment, we derive new quantitative

insights on the impact of the financing link on investment.

The remainder of this paper is organized as follows. In Section 2, we present the

R-model, which is solved in Section 3. Section 4 analyzes the R-model. In Section 5, we

6

use the R-model to explain empirically observed renegotiation patterns, credit spreads,

covenant structures, and financial policies. Finally, Section 6 concludes.

2. The model

Our structural framework is in the spirit of Mello and Parsons (1992) and the extension

for investment by Hackbarth and Mauer (2012). The novel feature of the model is that

we incorporate not only the possibility of distressed reorganization as suggested by Fan

and Sundaresan (2000), but also the ability to renegotiate a covenant outside distress.

In the following, we present the R-model. We first describe the firm’s assets in place

and the investment opportunity. Next, we discuss the covenant, debt covenant renegoti-

ation, and the financing of investment. Finally, we present distressed reorganization.

2.1. Assumptions

Assets are continuously traded in complete and arbitrage-free markets. Investors may

lend and borrow at the risk-free rate r. Corporate taxes are paid at a constant rate τ on

operating cash flows, and full offsets of corporate losses are allowed. Firms act in the best

interest of equity holders and choose the investment policy to maximize equity value.

The firm’s assets in place and investment opportunity. We consider an infinitely

lived firm with assets in place and an investment opportunity. At each time t, assets in

place generate a cash flow Xt. The cash flow Xt constitutes the exogenous state variable.

Following Grossman and Hart (1986) and Bolton and Scharfstein (1996), we assume that

Xt is observable, but not verifiable by courts or other outside parties. Hence, an ex-

ante contract specifying, for example, financing or investment policies contingent on cash

flows is not feasible because courts cannot enforce it. This assumption is standard in the

debt overhang literature (e.g., Bhattacharya and Faure-Grimaud, 2001; Favara, Morellec,

Schroth, and Valta, forthcoming). The cash flow Xt of the firm follows a geometric

Brownian motion under the risk-neutral probability measure Q

dXt = µXtdt+ σXtdWt, X0 > 0, (1)

in which µ is the drift, σ the volatility, and Wt a Brownian motion under Q.

7

In practice, investment financing is an important motive of covenant renegotiations

(Roberts, 2015). Hence, we incorporate an investment that generates funding needs. The

investment opportunity is modeled as an American call option on the firm’s cash flow,

analogous to Hackbarth and Mauer (2012). Specifically, if equity holders decide to invest

at time t, an investment cost I must be paid to receive an additional future cash flow

of (s− 1)Xt for some factor s > 1 for all future times t ≥ t. After investment, the firm

consists of only invested assets. The investment decision is irreversible. In reality, many

investment opportunities are not perfectly correlated to existing assets or may occur and

disappear randomly. Our investment specification is a simplification to investigate the

impact of investment funding needs on debt renegotiation in a tractable fashion.

Initially, the firm is financed by issuing equity and private debt of infinite maturity.

Private debt is one of the largest if not the largest source of funds for U.S. corporations

(Krishnaswami, Spindt, and Subramaniam, 1999; Denis and Mihov, 2003). While in

practice renegotiations occur also with public bonds, they are more costly, have a higher

exposure to free-rider problems, and are more difficult to coordinate than renegotiations

with private debt holders (Rajan, 1992; Krishnaswami, Spindt, and Subramaniam, 1999).1

After initial debt is issued, the firm pays a total coupon rate cA0 to initial debt holders

(A). The firm also pays corporate taxes at a constant rate τ . If the required debt service

exceeds the cash flow, shareholders can inject funds to finance the coupon. Alternatively,

shareholders have the possibility to default on their debt obligations (Leland, 1998), in

which case the firm is immediately liquidated. Debt holders enjoy absolute priority of

their claims. As in Hackbarth and Mauer (2012), debt holders obtain the unlevered value

of assets in place times the recovery rate α, whereas the investment option is lost in

default.2

Debt covenant renegotiation and the financing of investment. We allow the firm to

install a covenant in the initial debt contract that prevents the issuance of additional

debt. Covenants restricting new debt financing are ubiquitous in debt contracts of real

firms (e.g., Smith, Jr. and Warner, 1979, Bradley and Roberts, 2015). A covenant

specifying future debt financing contingent on cash flows is not feasible because Xt is not

1Changes to covenants, for example, must be approved by bondholders representing no less thantwo-thirds of the total principal. Such a majority approval is difficult in the case of diffusely held publicbonds because the Trust Indenture Act of 1939 gives the trustees in public bond issues only limiteddiscretion during renegotiation outside bankruptcy.

2Alternatively, we can assume that only a fraction of the investment opportunity is lost in default andthat the remaining fraction of the investment opportunity may or may not be levered up in the future.These alternative assumptions have only minor impact on the results.

8

verifiable by courts. Therefore, we consider a covenant that restricts the issuance of any

additional debt. Empirical and theoretical evidence shows that debt restructuring occurs

commonly upon lumpy investment (Dudley, 2012; Hackbarth and Mauer, 2012) and that

firms initiate covenant modifications primarily to alter investment, operating, or financing

policies (Roberts, 2015). Hence, we incorporate that equity holders can renegotiate the

covenant with debt holders upon investment to finance the investment cost through both

additional equity and new debt. Specifically, debt holders agree to waive the covenant in

exchange for a compensation offered by equity holders. The total compensation required

by debt holders includes both the full compensation for the dilution of initial debt due

to the issuance of new debt and part of the renegotiation surplus associated with the

additional tax shield of new debt. The compensation to initial debt holders consists of an

additional compensation coupon such that the total coupon (after investment) to initial

debt holders is cA01 = cA0 +cA1 ≥ cA0 . Changes in interest rate at renegotiations are common

in practice. Roberts and Sufi (2009b), for example, find that 55% of renegotiations entail

alteration of the coupon, with an average change of 64 bps in interest rate spread, or 40%

of the initial spread. Several contract terms such as amount and maturity are usually

renegotiated along with the interest rate (Denis and Wang, 2014). In real non-distressed

covenant renegotiations, debt holders can typically negotiate a change in contract terms

that improves the value of their claim (Kahan and Rock, 2009; Feldhutter, Hotchkiss,

and Karakas, forthcoming). Our compensation coupon captures this observation in a

tractable fashion. In Section 3.3, we show that the mean of the compensation does not

alter the model’s solution and results and that the assumption of compensation via an

interest rate alteration is therefore without loss of generality. The coupon to new debt

holders (B) after renegotiation is denoted by cB1 . The sum of the values of new debt and

new equity corresponds to the investment cost I.

Debt covenant renegotiation constitutes a simple approach through which firms can

relax the financing friction of covenants in place. While several alternative channels

can remove a covenant, they are costly to firms. Repaying callable or short term debt,

for example, entails restructuring costs (e.g., Christensen, Flor, and Miltersen, 2014)

and search frictions to obtain new financing (e.g., Hugonnier, Malamud, and Morellec,

2015). Violating a covenant without the consent of the creditors imposes serious conse-

quences on firms’ investment and financing policies, collateral requirements, monitoring

and reporting frequencies, ratings, CEO turnover, and interest rate spreads (e.g., Chava

and Roberts, 2008; Nini, Smith, and Sufi, 2009). These consequences could explain why

9

covenant renegotiations occur more frequently than covenant violations (Denis and Wang,

2014). For tractability, we assume that the alternative channels to remove a covenant are

prohibitively costly.

When equity holders decide to invest, the new capital structure is determined as

the Nash solution to the renegotiation game. The renegotiation game is characterized as

follows. Debt holders can enforce the prevailing covenant and prevent equity holders from

issuing additional debt, which constitutes the outside option or disagreement point of the

renegotiation game. We assume that the outside option of equity holders is to immediately

invest and finance the cost by issuing equity only. The Nash solution determines the

sharing rule between equity and debt holders for the surplus from financing the investment

cost by issuing a mix of debt and equity as opposed to financing with an equity issuance

only. While equity holders receive surplus through the issue proceeds of new debt, the

initial debt holder’s surplus is obtained through the compensation coupon. Hence, the

sharing rule corresponds to the combination of coupons{cA1 , c

B1

}given the initial coupon

cA0 . Equity holders’ bargaining power is denoted by η, and, hence, debt holders’ bargaining

power is given by 1− η.

Reorganization: Debt renegotiation in corporate distress. We model a distressed re-

organization as a debt-equity swap following Fan and Sundaresan (2000). In particular,

if cash flows deteriorate, equity holders offer debt holders to swap their original debt

against equity. A disagreement triggers immediate default as described above, inducing

a loss of the investment opportunity and a fraction 1−α of the unlevered value of assets

in place. Thus, the firm’s claim holders have an incentive to reorganize to avoid these

default costs. The fraction of equity offered to debt holders in exchange for their debt,

denoted by 1−θ, corresponds to the Nash solution. A distressed debt-equity swap implies

that the firm becomes an all-equity firm, and, in particular, it loses its tax shield. Hence,

while corporate taxes encourage debt financing by shielding part of a firm’s cash flow

from taxation, distressed reorganization limits the incentive to issue debt.

Figure 1 presents the timeline of the model. Reorganization can occur before or af-

ter investment. We assume that the option to invest is preserved in case of previous

reorganization. That is, if equity holders first reorganize after firm initiation (“initial

reorganization”), they may still invest later. If equity holders invest subsequently (“in-

vestment after initial reorganization”), they issue new debt to finance investment. Equity

10

holders can again decide to reorganize this new debt (“reorganization after investment

following reorganization”) in case of distress.

INSERT FIGURE 1 HERE

If reorganization occurs after covenant renegotiation at investment (“reorganization

after investment”), the fraction 1 − θ of the unlevered firm value is offered jointly to

initial and new debt holders. We assume that this fraction 1 − θ is shared between

initial and new debt holders in proportion to the value of their respective coupons. That

is, initial debt holders receive a fraction (1− θ1) cA01cA01+c

B1

and new debt holders receive a

fraction (1− θ1) cB1cA01+c

B1

of the unlevered firm value. This sharing rule is motivated by

equal priority of debt claims. Section 3 shows that value functions and corporate policies

are not affected by this sharing rule.

3. Model solution

Figure 1 illustrates the use of subscripts in the model timeline. Value functions and

parameters after firm initiation but before covenant renegotiation at investment or initial

reorganization carry a subscript 0. After covenant renegotiation at investment or after

initial reorganization, we use a subscript 1. To distinguish between these two cases,

the additional subscript l (l for low) labels value functions after initial reorganization,

while the subscript h (h for high) labels value functions after covenant renegotiation at

investment. Value functions and parameters after reorganization following investment

and after investment following reorganization carry a subscript 2. Finally, a subscript 3

indicates the case in which a firm has reorganized twice (reorganization after investment

following initial reorganization).

The model is solved by backward induction. First, Section 3.1 calculates the value

functions after the initial reorganization. These calculations include the solution to the

final reorganization game and the investment decision after initial reorganization. Next,

we derive the value functions and reorganization policy after covenant renegotiation at

investment (Section 3.2). Subsequently, Section 3.3 defines and solves the bargaining

game of covenant renegotiation determining the compensation coupon to initial debt

holders and the coupon of new debt. Finally, we solve for the value functions of corporate

11

securities before covenant renegotiation or distressed reorganization (Section 3.4), and

determine the initial reorganization threshold, the investment boundary at which the

covenant is renegotiated, and the optimal initial capital structure (Section 3.5).

3.1. Initial reorganization and the value functions thereafter

The value functions after investment following reorganization correspond to the case ana-

lyzed in Fan and Sundaresan (2000). An overview of the final reorganization is presented

in the following, while further details can be found in Appendix A.

We start by considering the reorganization after investment following reorganization.

Denote this reorganization boundary by S2. In this reorganization game, the outside

option is that equity holders default on their debt obligation and debt holders receive the

unlevered after-tax asset value net of default costs. The unlevered after-tax asset value

is calculated as

v3 (X) =1− τr − µ

X. (2)

Following Fan and Sundaresan (2000), the sharing rule 1 − θ2, i.e., the fraction of the

unlevered assets offered to debt holders in exchange for their claim, is determined as the

Nash solution to the final reorganization game

θ2 = arg max0≤θ2≤1−α

{θ2v3 (S2)− 0

}η {(1− θ2

)v3 (S2)− αv3 (S2)

}1−η(3)

= η (1− α) . (4)

The final reorganization boundary as well as the value functions for debt and equity after

investment following reorganization are presented in closed form in Appendix A.

Next, we consider the period after initial reorganization but before investment. Denote

the corresponding investment threshold by U1. In this case, the firm is all-equity financed

with the option to simultaneously invest and relever.

Using the closed-form solution for the firm value after investment following reorgani-

zation (see Appendix A), we calculate the investment boundary U1 in closed form as

U1 =β1

β1 − 1

(r − µ) I

(s− 1) (1− τ) + sτ (1− β2)1β2 (1− θ)

, (5)

12

in which

β2 =1

2− µ

σ2−

√(1

2− µ

σ2

)2

+2r

σ2. (6)

The value of equity, e1l (X) , corresponds to the firm value calculated in closed form in

Appendix A.

Next, we consider the initial reorganization. Denote the initial reorganization bound-

ary by S0. The outside option is that equity holders default on their debt obligation, and

debt holders receive the unlevered value of assets in place net of default costs. That is, the

outside option is given as a fraction α of the unlevered asset value v1 (X) = 1−τr−µX. The

sharing rule 1−θ0, i.e., the fraction of the unlevered asset value offered to debt holders in

exchange for their claim in the initial reorganization, is determined as the Nash solution

to the initial reorganization game

θ0 = arg maxθ0

{θ0e1l (S0)− 0

}η {(1− θ0

)e1l (S0)− α

1− τr − µ

S0

}1−η

. (7)

In Appendix A, we show that the sharing rule to this reorganization game is given as

θ0 = η

(1− α v1 (S0)

e1l (S0)

). (8)

Eq. (8) reveals that the fraction 1 − θ0 offered to debt holders in exchange for their

claim depends on the reorganization boundary S0. The functional form of the solution

to θ0 differs from the functional form of the solution to the reorganization game after

investment following reorganization θ2, which is a constant determined by Eq. (4). The

reason for this difference is that the outside option of initial reorganization determining

Eq. (7) implies that the investment opportunity and a fraction of the unlevered assets

are lost. Conversely, the outside option of the final reorganization determining Eq. (3)

reflects that only a fraction of the unlevered asset value is lost.

13

3.2. Value functions after covenant renegotiation at investment

Reorganization after covenant renegotiation is analogous to the final reorganization after

investment following reorganization. Hence, the Nash solution is

θ1 = η (1− α) , (9)

as in Fan and Sundaresan (2000). Let d1h(·; cA01

), d1h

(·; cB1

), and e1h

(·; cA01 + cB1

)denote

the value of initial debt, new debt, and equity, respectively, after covenant renegotiation

at investment. Because of the existence of two creditors at this stage, we explicitly write

the dependence of the coupon. S1 is the reorganization boundary for the debt-equity

swap after covenant renegotiation at investment. The value functions of total debt and

equity are calculated in Fan and Sundaresan (2000). They are analogous to the case of

investment after initial reorganization (see Section 3.1). We provide the full solution to

these value functions in Appendix B.

3.3. Debt covenant renegotiation and investment

The threshold triggering covenant renegotiation at investment is denoted by U0. We

define the sharing rule as{cA01, c

B1

}, i.e., as the total coupon to initial debt holders and

the coupon of new debt whose issue proceeds accrue to equity holders. The surplus

to equity from covenant renegotiation is the difference between the values of equity in

renegotiation and in disagreement. The value of equity at covenant renegotiation is the

total value of equity given the cash flow after investment and the total new coupon

plus the issue proceeds from new debt less the investment cost. The value of equity in

disagreement corresponds to the total value of equity given the cash flow after investment,

but a coupon equal to the initial coupon less the investment cost. Hence, the surplus to

equity holders at covenant renegotiation, SE(U0; c

A01, c

B1

), is

SE(U0; c

A01, c

B1

)= e1h

(sU0; c

A01 + cB1

)+ d1h

(sU0; c

B1

)− I −

(e1h(sU0; c

A0

)− I)

= e1h(sU0; c

A01 + cB1

)+ d1h

(sU0; c

B1

)− e1h

(sU0; c

A0

). (10)

Similarly, we calculate the surplus to debt holders as the difference between the value of

debt at covenant renegotiation and the value of debt in disagreement. Upon covenant

renegotiation, equity holders promise initial debt holders an additional compensation

14

coupon of cA01 − cA0 > 0. In disagreement, the coupon to debt holders remains unchanged

at the initial coupon. Hence, the surplus to debt holders, SD(U0; c

A01, c

B1

), is

SD(U0; c

A01, c

B1

)= d1h

(sU0; c

A01

)− d1h

(sU0; c

A0

). (11)

{cA01, c

B1

}is determined as the Nash solution to the covenant renegotiation game:

{cA01, c

B1

}= arg max

{cA01,cB1 }

{SE

(U0; c

A01, c

B1

)}η {SD

(U0; c

A01, c

B1

)}1−η= arg max

{cA01,cB1 }

{e1h(sU0; c

A01 + cB1

)+ dB1h

(sU0; c

B1

)− e1h

(sU0; c

A0

)}η·{d1h(sU0; c

A01

)− d1h

(sU0; c

A0

)}1−η, (12)

in which we used Eqs. (10) and (11). The total surplus, ST(U0; c

A01, c

B1

), is calculated as

ST(U0; c

A01, c

B1

)= SE

(U0; c

A01, c

B1

)+ SD

(U0; c

A01, c

B1

)(13)

= e1h (sU0; c1) + d1h(sU0; c

B1

)+ d1h

(sU0; c

A01

)(14)

−e1h(sU0; c

A0

)− d1h

(sU0; c

A0

)= f1h (sU0; c1)− e1h

(sU0; c

A0

)− d1h

(sU0; c

A0

), (15)

in which f1h (·) denotes the firm value after covenant renegotiation at investment. The

following Proposition 1 presents the basic properties of the Nash solution to the covenant

renegotiation game. All proofs can be found in the Appendix.

Proposition 1. If initial debt carries a renegotiable covenant preventing the issuance of

new debt, the Nash solution to the covenant renegotiation game

{cA01, c

B1

}= arg max

{cA01,cB1 }

{e1h(sU0; c

A01 + cB1

)+ dB1h

(sU0; c

B1

)− e1h

(sU0; c

A0

)}η·{d1h(sU0; c

A01

)− d1h

(sU0; c

A0

)}1−η, (16)

exhibits the following properties:

(i) The total coupon c1 = cA01 + cB1 determined by the Nash solution corresponds to the

first-best coupon cfb1 maximizing the value of the firm, i.e.,

c1 = cfb1 =r

r − µβ2 − 1

β2(1− β2)

1β2 (1− θ) sU0. (17)

15

Further, the total surplus from covenant renegotiation, ST(U0; c

A01, c

B1

), depends on

the coupons cA01 and cB1 only through c1, i.e., the sum of the coupons to initial and

new debt holders. It is given by

ST(U0; c

A01, c

B1

)= ST (U0; c1) = f fb1h (sU0)− e1h

(sU0; c

A0

)− d1h

(sU0; c

A0

), (18)

in which f fb1h (sU0) denotes the first-best firm value at the cash flow level sU0.

(ii){cA01, c

B1

}is such that the surplus from covenant renegotiation to initial debt hold-

ers, SD(U0; c

A01, c

B1

), and the surplus from covenant renegotiation to equity holders,

SE(U0; c

A01, c

B1

), satisfy

SE(U0; c

A01, c

B1

)= ηST (U0; c1) (19)

SD(U0; c

A01, c

B1

)= (1− η)ST (U0; c1) , (20)

i.e., the two parties receive a fraction of the total surplus corresponding to their

respective bargaining power.

Proposition 1 is intuitive. Property (i) states that covenant renegotiation leads to first-

best leverage at investment. The reason is Pareto efficiency of the Nash solution. Property

(ii) shows that the total renegotiation surplus is shared according to the bargaining power

of the two parties.

The properties of the Nash solution to the covenant renegotiation game are robust to

the assumptions on the sharing rule of equity in reorganization between initial and new

debt holders as well as to the mean of compensation to initial debt holders upon renegoti-

ation. Specifically, the presented model assumes that at reorganization after investment,

equity is assigned to debt holders according to the fraction of their respective coupon.

That is, initial [new] debt holders obtain a fraction (1− θ1) cA01cA01+c

B1

[(1− θ1) cB1cA01+c

B1

] of total

equity. Further, we assume that initial debt holders are compensated with an additional

coupon cA01− cA0 . Proposition 1 remains valid with alternative assumptions. For example,

the assumption that initial debt holders are compensated with a one-time payment at

covenant renegotiation still yields first-best leverage at investment and a sharing of the

renegotiation surplus proportional to the claimants’ bargaining power.

16

3.4. Value functions before covenant renegotiation or initial re-

organization

In this section, we present the value functions before covenant renegotiation or initial

reorganization for equity and corporate debt, denoted by e0 (X) and d0 (X), respectively.

The reorganization threshold is denoted by S0, and the boundary for covenant renegoti-

ation at investment is denoted by U0.

Proposition 2. (i) The value of equity in the continuation region S0 ≤ X ≤ U0 is

given by

e0 (X) = Ae00 + Ae01 X + Ae02 Xβ1 + Ae03 X

β2 , (21)

in which

β1,2 =1

2− µ

σ2±

√(1

2− µ

σ2

)2

+2r

σ2, (22)

Ae00 = −(1− τ) cA0r

, Ae01 =1− τr − µ

. (23)

Ae02 , Ae03 jointly solve the system

M[Ae02 Ae03

]T= be0 , (24)

in which

M =

[Sβ10 Sβ20

Uβ10 Uβ2

0

], (25)

be0 =

[−Ae00 − Ae01 S0 + θ0e1l (S0)

ηF1hsU0 + (1− η) e1h(sU0; c

A0

)− ηd1h

(sU0; c

A0

)− Ae00 − Ae01 U0

]. (26)

F1h is the factor to calculate the first-best firm value (f1h (X) = F1hX), i.e.,

F1h =[1− τ + τ (1− β2)

1β2 (1− θ)

] 1

r − µ, (27)

and e1l (·) is given in closed form in Appendix B, Eqs. (58)-(60).

(ii) The value of corporate debt in the continuation region S0 ≤ X ≤ U0 is given by

d0 (X) = Ad00 + Ad02 Xβ1 + Ad03 X

β2 , (28)

17

in which β1,2 are defined in Eq. (22) and

Ad0 =cA0r. (29)

Ad2, Ad3 jointly solve the system

M[Ad2 Ad3

]T= bd, (30)

in which

M =

[Sβ10 Sβ20

Uβ10 Uβ2

0

], (31)

bd =

[−Ad0 + (1− θ0) e1l (S0)

(1− η)F1hsU0 + (1− η) e1h(sU0; c

A0

)− ηd1h

(sU0; c

A0

)− Ad0

]. (32)

F1h is as in Eq. (27) and Appendix B, Eqs. (58)-(60) states e1l (·) in closed form.

The values of initial debt and equity are independent of our assumptions on the

equity sharing rule in reorganization between initial and new debt holders as well as of

the mean of compensation to initial debt holders upon covenant renegotiation. The reason

is that the properties of the Nash solution are robust to alternative assumptions. For

example, a sharing rule in reorganization less favorable for initial debt holders entails an

increase in compensation coupon. However, the Nash solution requires that the increase

in compensation coupon lead to the same surplus as with a proportional sharing rule.

Therefore, the values of equity and initial debt remain constant.

3.5. Reorganization threshold, renegotiation boundary, and cap-

ital structure

For a given initial coupon cA0 , equity holders solve

{S0, U0} = arg maxS0,U0

e0 (X) . (33)

18

The boundary conditions for equity are

e0 (S0) = θ0e1l (S0) (34)

e0 (U0) = e1h (sU0; c1)−(I − d1h

(sU0; c

B1

)). (35)

Hence, the smooth-pasting conditions read

∂

∂Xe0 (X) |X=S0 = η

∂

∂Xe1l (X) |X=S0 − ηα

1− τr − µ

(36)

∂

∂Xe0 (X) |X=U0 = ηf1hs+ (1− η)

∂

∂Xe1h(sX; cA0

)|X=U0 − η

∂

∂Xd1h(sX; cA0

)|X=U0(37)

in which θ0 is inserted as given in Eq. (7). Recall that e1l (·) , e1h(·; cA0

), and d1h

(·; cA0

)as well as their partial derivatives are available in closed form. Finally, equity holders

choose the initial capital structure by maximizing the value of their objective function

ex-ante. Hence, equity holders solve

cA0 = arg maxcA0

{e0 (X0) + d0 (X0)} , (38)

subject to Eqs. (36)-(37). A closed-form solution does not exist. We use numerical

procedures and verify the optimality of the renegotiation and reorganization boundaries

numerically.

4. Model analysis

In this section, we derive the main implications of the covenant renegotiation feature for

corporate policies and firm value.

4.1. Baseline parameter selection

We use baseline parameter values to reflect a typical S&P 500 firm. The risk free interest

rate is r = 5%, the risk-neutral growth rate of the cash flows µ = 3%, the volatility of the

cash flow σ = 23%, the tax advantage of debt τ = 15%, and the recovery rate α = 60%.

The initial cash flow is normalized to X0 = 1. The bargaining power of equity holders is

set to η = 0.5, as in the base case of Fan and Sundaresan (2000).

19

For the investment opportunity, we choose an investment cost of I = 20. A scale

parameter s = 1.8 implies an initial market-to-book ratio of 1.62 for our baseline firm,

which closely reflects the average in our empirical sample of firms with private credit

agreements from Nini, Smith, and Sufi (2009). The initial market-to-book ratio of a

model firm is calculated by dividing the market value of the firm by the value of invested

assets.

4.2. Impact of a renegotiable covenant

Table I compares corporate policies and firm values in different models and for various

parameters. The NR-model has no debt renegotiation or covenant (cf. Hackbarth and

Mauer, 2012). The FSI-model is the distressed reorganization model of Fan and Sundare-

san (2000) augmented for investment as in Hackbarth and Mauer (2012). Equity holders

choose investment, financing, and distressed reorganization policies that maximize the

ex-post value of their claim. The FSI-model is similar to the model of Sundaresan and

Wang (2007), the only difference being that parties in the latter model renegotiate con-

tractual coupon payments instead of a debt-equity swap. The FSI-first-best corresponds

to the FSI-model but applies investment and financing policies to maximize firm value.

Equity holders choose the distressed reorganization policy. Details of the FSI-first-best

model are presented in Appendix F. In the FSI-model, equity holders issue excessive

new debt at investment (overleverage): the leverage at investment is 72% in the FSI-

model, whereas it is only 63% in the FSI-first-best. The reason is that equity holders

do not internalize the impact of the increased distressed reorganization risk associated

with issuing new debt on the value of initial debt, but fully benefit from the additional

tax shield. Because the investment and restructuring benefit at investment accrues to

equity holders, and due to the transfer of wealth from initial debt to equity holders (ex-

propriation) owing to the large issuance of new debt, equity holders also invest too soon

(overinvestment). In particular, the renegotiation (investment) boundary declines from

2.76 in the FSI-first-best to 1.94 in the FSI-model. The FSI-model firm implements a

lower initial coupon and, hence, a smaller tax shield than the FSI-first-best firm because

the overleverage at investment and overinvestment problems render initial debt more ex-

pensive. Due to these agency costs of debt, the value of the FSI-first-best firm is 2.15%

above that of the FSI-model. Qualitatively, the presented agency costs also arise without

distressed reorganization, as shown in Hackbarth and Mauer (2012). In the framework

20

with distressed reorganization, however, they are larger, primarily because firms with the

possibility of distressed reorganization choose a higher initial coupon ex-ante owing to

their ability to avoid costly default through reorganization. This higher coupon enlarges

the agency cost of debt.

The gross benefit to firms of installing a renegotiable financing covenant in the initial

debt contract consists of mitigating the agency costs of debt. In particular, a renegotiable

covenant solves overleverage at investment, as shown in Proposition 1. It also mitigates

the large investment distortion (overinvestment) because renegotiation prevents expropri-

ation of initial debt holders. Without overleverage at investment and smaller investment

distortion, a firm implements a larger initial coupon. We measure the benefit from the

mitigation of total agency costs of debt as the difference between the FSI-first-best and

FSI-model firm values. As shown in column GB, this benefit corresponds to 2.15%.

Including a financing covenant also entails a cost. In the FSI-models, equity holders

capture the investment benefit, which includes the value of exercising the investment

opportunity plus the additional tax shield of new debt less the investment costs. Fur-

ther, the issuance of new debt at investment transfers wealth from initial debt to equity

holders. If equity holders reorganize with a debt-equity swap before investment, they

must share the future investment benefit with initial debt holders who obtain part of the

equity in this swap. Furthermore, equity holders lose the ex-post wealth transfer facility

because the firm is all equity financed at investment. To maintain the opportunity to

capture the investment benefit and transfer wealth, equity holders’ incentive to reorga-

nize before investment is relatively weak. In the R-model, equity holders need to share

the renegotiation surplus with initial debt holders and, hence, cannot transfer wealth at

investment. Therefore, if equity holders reorganize before investment, the value of the

opportunity they lose is smaller than that in the FSI-model. Hence, the reorganization

risk in the R-model is larger than that in the FSI-model. Higher distressed reorganization

risk reduces firm value as the tax shield earned between reorganization and investment

is lost in case of reorganization and because firms install a lower initial coupon.

To quantify the value loss of the higher distressed reorganization risk caused by the

ability of covenant renegotiation, we calculate the “R-first-best” in the fourth line of

Panel A. The R-first best corresponds to the R-model but applies firm-value maximizing

investment and financing policies. Equity holders, however, choose the distressed reorga-

nization policy. Details of the R-first best are presented in Appendix F. The difference

21

Table IThe impact of a renegotiable financing covenant

This table shows the impact of a renegotiable financing covenant on firm value and policies fordifferent parameters. Panel A displays the baseline results. In Panel B–G, one parameter is changed ata time. η is the bargaining power of equity holders, s the scale parameter of the investment opportunity,τ the corporate tax rate, α the recovery rate at default, σ the volatility of cash flow, and µ the cashflow drift. The NR-model is a model without debt renegotiation but with investment as presentedin Hackbarth and Mauer (2012). The FSI-model is the distressed reorganization model of Fan andSundaresan (2000) augmented for investment. Equity holders choose the financing, investment, andreorganization policies to maximize the value of their claim in this model. The FSI-first-best correspondsto the FSI-model but applies firm-value maximizing investment and financing policies. The R-modelconsiders a firm with distressed reorganization and a renegotiable covenant. The R-first-best correspondsto the R-model but applies firm-value maximizing investment and financing policies; however, equityholders choose the distressed reorganization policy. S0 is the reorganization boundary, U0 the investmentboundary initiating covenant renegotiation in the R-models, and cA0 the initial coupon. levU and lev0 areleverage at investment and initial leverage, respectively, and f0 is the initial firm value. GB is the grossbenefit and C the cost of a renegotiable covenant. Gross benefit is defined as the total agency costs ofdebt in the FSI model, and cost is the value loss due to increased reorganization risk and underinvestmentin the R-model. The net benefit of covenant renegotiation, NB, is defined as the percentage firm value

increase of the R-model compared to the FSI-model, i.e., NB = 100 ·(

1− fC0

fFSI0

).

S0 U0 cA0 levU lev0 f0 GB C NB

Panel A: Baseline parameters, optimal initial couponNR-model 0.21 2.28 1.19 0.57 0.31 66.49FSI-model 0.25 1.94 1.08 0.72 0.26 67.73FSI-first-best 0.53 2.76 2.40 0.63 0.53 69.19 2.15R-first-best 0.53 2.70 2.19 0.63 0.54 68.99 2.15 –0.29R-model 0.52 2.78 2.19 0.63 0.53 68.99 2.15 –0.29 1.86

Panel B: Higher bargaining power (η = 0.75)FSI-model 0.29 2.00 1.00 0.63 0.24 67.06R-model 0.51 2.75 1.68 0.56 0.42 67.89 1.44 –0.21 1.24Panel C: Higher scale parameter (s = 2.2)FSI-model 0.13 1.40 0.61 0.69 0.12 82.39R-model 0.50 1.98 2.36 0.63 0.49 83.73 1.91 -0.29 1.63Panel D: Higher tax rate (τ = 0.2)FSI-model 0.35 2.01 1.55 0.73 0.37 66.15R-model 0.53 2.96 2.18 0.65 0.55 67.30 2.24 –0.49 1.75Panel E: Higher recovery rate (α = 0.9)FSI-model 0.24 1.88 1.18 0.84 0.28 68.68R-model 0.52 2.82 2.51 0.74 0.60 70.19 2.55 –0.34 2.20Panel F: Higher volatility of cash flows (σ = 0.25)FSI-model 0.23 2.03 1.06 0.71 0.25 68.03R-model 0.51 2.99 2.28 0.63 0.53 69.32 2.21 –0.31 1.90Panel G: Lower cash flow drift (µ = 0.02)FSI-model 0.30 2.08 0.86 0.73 0.33 40.97R-model 0.51 2.79 1.40 0.63 0.54 41.60 1.82 –0.30 1.53

22

between this firm value and the FSI-first-best firm value quantifies the impact of the

R-model’s larger reorganization risk. With baseline parameters, it is –0.29%, as shown

in column C.

Corporate policies with a renegotiable covenant in the R-model are shown in the

last line of Panel A. The difference between the R-first-best and R-model is that equity

holders choose all corporate policies to maximize the value of their claim in the latter

case. Because initial debt holders capture part of the renegotiation surplus at investment,

equity holders invest somewhat too late compared to a policy maximizing firm value

(underinvestment). The quantitative impact of this investment timing friction in the R-

model, however, is very limited. In particular, firm values rounded to two decimals are

equal in the R-first-best and R-model in the base case.

The benefit of a renegotiable covenant dominates the cost such that the firm value

increases by 1.86% (2.15%–0.29%) in the R-model compared to the FSI-model. This

net benefit measures the quantitative importance to firms of including a renegotiable

covenant. We tabulate this net benefit in the last column NB of Table I.

We also calculate the total value of the ability to renegotiate debt to firms. In the

NR-model without any renegotiation in line one of Panel A of Table I, we obtain a

firm value of 66.49. Adding distressed reorganization increases firm value by 1.87% to

67.73 (FSI-model in Panel A), mainly because reorganization avoids default costs. With

an additional renegotiable covenant in the R-model, the firm value increases by 3.76% to

68.99. In this case, the possibility to renegotiate debt avoids default costs and reduces the

agency costs of debt. These numbers show that incorporating non-distressed renegotiation

more than doubles the impact of the possibility to renegotiate debt on firm value. Hence,

the neglect of covenant renegotiation severely underestimates the value of firms’ ability

to renegotiate debt.

Firm parameters influence the magnitude of the benefit and cost of a renegotiable

covenant and, hence, the value to firms of installing a covenant. To explore this influence,

we change one parameter in each Panel B–G of Table I and report the resulting corporate

policies and firm values.

We start by analyzing how bargaining power affects our results in Panel B of Table I.

The response of firms to a larger η is to reduce the initial coupon. With a lower initial

coupon, the agency costs of debt become smaller. Thus, the benefit of a renegotiable

23

covenant declines compared to Panel A (column GB). Reduction in initial coupon also

mitigates the distressed reorganization risk and, therefore, the cost of a renegotiable

covenant (column C). The decline in benefit is stronger than that of the cost. Therefore,

the net benefit of a renegotiable covenant is smaller than that in Panel A.

Table I also shows that firm value is more sensitive to bargaining power in the R-

than the FSI-model. For instance, Panels A and B imply that the FSI-model’s firm value

declines by 0.99% when η raises from 0.5 to 0.75 from the increase in distressed reorgani-

zation risk. The R-model’s firm value decreases by 1.46%. This decline is stronger than

that in the FSI-model mainly because the benefit of a renegotiable covenant diminishes

with η.

Similar to Panel B, a larger scale parameter of the investment opportunity in Panel

C reduces the optimal initial coupon, which decreases both the benefit and cost of a

renegotiable covenant. The decline in benefit is stronger than that of the cost such that

the net benefit of a renegotiable covenant is smaller than that in Panel A.

We also analyze the impact of an increase in tax rate in Panel D. A higher tax rate

increases the cost of a renegotiable covenant for two reasons. First, the investment benefit

of issuing new debt rises, which increases the difference between the FSI- and R-models’

distressed reorganization risk. Second, the expected loss in tax shield due to higher

reorganization risk in the R-model has a larger value when the tax rate increases. As

the benefit of a renegotiable covenant changes only slightly with a higher tax rate, the

increase in cost dominates. Thus, the value of a renegotiable covenant is smaller in Panel

D than in Panel A, as shown in column NB.

The larger recovery rate in Panel E raises the optimal initial coupon compared to Panel

A, which increases both the benefit and cost of a renegotiable covenant. Further, equity

holders have a stronger incentive to avoid distressed reorganization in the FSI-model

when the recovery rate is larger because the fraction of equity that debt holders obtain

at distressed reorganization is higher. Thus, the difference in reorganization risk between

the R- and FSI-models increases, enlarging the cost of a renegotiable covenant. Overall,

the increase in benefit dominates the increase in cost, such that having a renegotiable

covenant is more important than in Panel A. Finally, Panels F and G in Table I show

that the value of a renegotiable covenant to firms increases with volatility and declines

with the cash flow drift.

24

5. Results and empirical predictions

The recognition that firms renegotiate both at distress and upon investment allows us to

explain empirically observed renegotiation patterns, credit spreads, covenant structures,

and financial policies. It also yields novel testable predictions.

5.1. Waiting times to renegotiation

We first investigate the model-implied expected waiting time from initiation to any rene-

gotiation (i.e., covenant renegotiation or distressed reorganization). To this end, we

calculate the expected waiting time in closed form (see Appendix G). The expected

waiting time to renegotiation for a baseline firm is 2.66 years.

As shown in Table I of Appendix G, firms with a more valuable investment opportu-

nity renegotiate the financing covenant at a lower threshold than firms with a less valuable

investment opportunity. Thus, the expected waiting time to covenant renegotiation de-

creases when the scale parameter s increases. Firms with a more valuable investment

opportunity, however, reorganize at a lower boundary than firms with a less valuable

investment opportunity (see Table I of the Appendix). Hence, the expected waiting time

to distressed reorganization increases with the scale parameter s. Thus, the question

of whether the expected waiting time to any renegotiation (covenant renegotiation or

distressed reorganization) decreases or increases with s is not trivial.

Figure 2 plots the expected waiting time to any renegotiation against the market-to-

book ratio, which is determined by the scale parameter s. It shows that the expected

waiting time is decreasing in the market-to-book ratio. The reason is that the negative

impact of s on the expected waiting time to covenant renegotiation dominates.

INSERT FIGURE 2 HERE

Since both the reorganization threshold and covenant renegotiation boundary are

decreasing in s, the conditional probability of covenant renegotiation, given any renego-

tiation, is increasing in s. To assess the importance of covenant renegotiation relative

to distressed reorganization, we calculate the conditional probability in closed form (see

25

Appendix G). As Figure 3 shows, the conditional probability of covenant renegotiation

is 41.4% in the baseline firm with a market-to-book ratio of 1.62.

INSERT FIGURE 3 HERE

With a market-to-book ratio of 2.4, the conditional probability of covenant renegoti-

ation is 71.4% and, thus, much higher than that of distressed reorganization. Even for

low market-to-book ratios, covenant renegotiations remain important. For example, a

market-to-book ratio of 1.2 still implies a conditional probability of covenant renegotia-

tion of about one quarter (25.6%).

Overall, the analysis suggests that covenant renegotiation contributes substantially to

the realized waiting times to renegotiation. This insight naturally leads to the question of

whether the R-model explains empirically observed debt renegotiation timing patterns.

We address this question in the next section.

5.2. Explaining empirical renegotiation patterns

We investigate the R-model’s ability to explain the renegotiation timing patterns reported

in the empirical literature. To this end, we adopt a simulation approach in the spirit of

Strebulaev (2007). The reasons for the simulation approach are twofold. First, the ex-

pected waiting times derived in the previous section are for optimally financed firms at

initiation. Firms in the real world, however, issue renegotiable debt at times other than

initiation. Thus, when a firm issues renegotiable debt, its capital structure, distance to

reorganization, and distance to covenant renegotiation typically differ from those of a

firm at initiation. These deviations can be represented in a simulation-based approach,

in which cash flows fluctuate over time. Second, Figures 2 and 3 show that the expected

waiting time to renegotiation as well as the conditional probability of covenant renegoti-

ation are non-linear in the market-to-book ratio. Due to these non-linearities, deviations

from the average market-to-book ratio do not translate linearly into deviations from the

average waiting time. Hence, it would be misleading to predict renegotiation patterns

in the cross section of empirical firms based on an average representative model-implied

firm.

To conduct the simulation, we first construct an empirical sample of a cross section

of firms. We collect the 3720 private credit agreements covered in Nini, Smith, and Sufi

26

(2009) from their home page. This sample has been analyzed by several papers with

regard to renegotiations (e.g., Roberts and Sufi, 2009b; Wang, 2013; Denis and Wang,

2014). It consists of all private loans in the Loan Pricing Corporation Dealscan database

extended to nonfinancial public firms from 1996 to 2005 with available Compustat infor-

mation for which the original credit agreements are available in SEC filings. We merge

this set with Compustat Data, which leaves us with 3688 observations, and we calculate

the average market-to-book and market leverage ratios for each observation over the four

previous quarters. The market-to-book ratio is constructed as Total Assets (item 44)

minus Book Equity plus Market Equity, scaled by Total Assets. Book Equity is Total

Assets minus Total Liabilities (item 54) minus Preferred Stock (item 55) plus Deferred

Taxes (item 52). Market Equity is the Equity Price (item 14) times Common Shares

Outstanding (item 61). The market leverage ratio is Book Debt, divided by Total Assets

minus Book Equity plus Market Equity. After dropping the firms with any missing data

over the four previous quarters, our final empirical sample consists of 3,070 private credit

agreements (“true cross section”) characterized by the market-to-book and leverage ratios

of the corresponding firm. Market leverage and market-to-book ratios are Winsorized at

the upper and lower 2.5 percentiles.

Next, we generate a model-implied sample of firms reflecting the true cross section,

following the simulation-based approach of Strebulaev (2007) as extended by Arnold,

Wagner, and Westermann (2013). For this purpose, we generate a large universe of

initially optimally financed model-implied firms. Specifically, we consider the firms for

which the initial scale parameter ranges from s = 1 to s = 2.95 using a step size of 0.05.

Firms with a scale parameter of s = 2.95 invest at a threshold of Xt = 1.13. Larger

scale parameters imply a high likelihood of almost immediate investment after initiation.

For each scale parameter s, we consider 100 initially identical firms. Thus, our universe

consists of 41,000 firms. This universe is simulated forward for ten years with a quarterly

frequency. We denote this procedure “pre-simulation.” Firms that reorganize or invest

are replaced by an optimally financed firm with an identical investment opportunity that

is not yet exercised. For each model-implied firm, the market-to-book ratio is the sum of

the book value of debt plus the market value of equity divided by the value of invested

assets, and the quasi-market leverage is given by the book value of debt divided by the

sum of the book value of debt plus the market value of equity. The book value of debt is

defined as the value of debt at initiation.

27

We now match the 3,070 observations in the true cross section with simulated, model-

implied firms. Specifically, for each observation in the true cross section, we select the

simulated firm at the end of the pre-simulation with the smallest squared sum of distances

with respect to leverage and market-to-book ratios. Thus, we obtain a sample of 3,070

model-implied matched firms.3

Using this model-implied matched sample, we investigate the timing patterns of debt

renegotiation. To this end, we simulate the matched sample forward with a quarterly

frequency. To maintain a balanced sample over time, we replace a reorganized or invested

firm by the corresponding firm at matching. That is, each replacement uses a firm with

an identical investment opportunity and cash flow as at the time of matching. We reflect

the average contract maturity of 46.7 months in Denis and Wang (2014) by choosing a

horizon of 48 months. The procedure is denoted as “post-simulation.” We report the

statistics of renegotiation patterns in this post-simulation.

We conduct the pre-simulation 100 times. For each pre-simulation, we consider 100

post-simulations, resulting in a total of 10, 000 simulations.

In general, our matching procedure is accurate. At matching, the square root of the

sum of squared distances between real firms and simulated sample firms with respect

to leverage and market-to-book ratios is 0.15 with an average cross sectional standard

deviation of 0.32. Table II shows the summary statistics for the true cross section from

Nini, Smith, and Sufi (2009), and for our simulated samples at matching. The matched

samples are structurally similar to the empirical sample. The main differences are due to

observations in the true cross section with very large market-to-book ratios that do not

match closely with the R-model.

Denis and Wang (2014) and Roberts and Sufi (2009b) report stylized facts about the

empirical renegotiation patterns in large, randomly selected subsamples of the sample

of Nini, Smith, and Sufi (2009). The statistics are summarized in columns one and two

of Table III. On average, slightly over 60% of contracts are renegotiated at least once,

and only around 18% of debt renegotiations are associated with corporate distress.4 The

reported time to the first renegotiation of contracts that are subsequently renegotiated is

3We also repeat the procedure by matching the book leverage and market-to-book ratios. The impacton our results is minor. Further, we verify that the matching outcome does not depend on the distributionof scale parameters s in the pre-simulation.

4Roberts (2015) and Wang (2013) confirm in their sample that most renegotiations are initiated byborrowers in response to changing conditions, rather than from lender interventions due to close default.

28

Table IISummary statistics of empirical and simulated samples at matching

This table shows the summary statistics for the true cross section from Nini, Smith, and Sufi (2009),and for the simulated model-implied samples at matching. The market-to-book ratio in the simulatedsamples is calculated as the sum of the book value of debt plus the market value of equity divided bythe value of invested assets, and the quasi-market leverage by the book value of debt divided by the sumof the book value of debt plus the market value of equity.

True cross Simulatedsection samples

Market-to-book ratio mean 1.69 1.65Market-to-book ratio median 1.39 1.39Market-to-book ratio standard deviation 0.90 0.67Market leverage mean 0.41 0.45Market leverage median 0.40 0.43Market leverage standard deviation 0.22 0.18

around 1.4 years. We calculate the average effective duration of an initial contract, i.e.,

the mean waiting time to the first renegotiation or final maturity (in case of contracts

not renegotiated) from the results presented in the papers mentioned above. The average

effective duration is 2.0 years in Denis and Wang (2014) and 1.5 years in Roberts and

Sufi (2009b).5 We obtain the effective duration and the duration in percentage of the

initially stated maturity from the results presented in Table 2 of Denis and Wang (2014).

The former measure is the average time to the first renegotiation or maturity expressed

in terms of initially stated maturity. The latter measure is the average time to any

renegotiation or maturity divided by the initially stated maturity, including renegotiations

after the first renegotiation. Roberts and Sufi (2009b) report this measure for their

sample. In both papers, the durations are around 60% of the initially stated maturity. We

additionally depict statistics on the renegotiation frequency illustrated in Denis and Wang

(2014). Conditional on being renegotiated, the average contract is renegotiated 2.7 times.

Figure 1 in their study also shows that around 37% of contracts are renegotiated just

once, 22% twice, and close to 13% three times. About 53% of contracts are renegotiated

between two and five times during their lifespan.

Next, we present the renegotiation patterns in the post-simulations of model-implied

samples. To assess the marginal contribution of covenant renegotiations, we first run our

5Roberts and Sufi (2009b) report a relatively large fraction of loans in their sample to disappear orreach the end of the sample without a renegotiation. They are, on average, characterized by long statedmaturities, which could explain part of the difference between the average effective durations in Denisand Wang (2014) and Roberts and Sufi (2009b).

29

Table IIIEmpirical and model-implied timing patterns of debt renegotiation

This table summarizes the key statistics on renegotiation timing. The first line shows the portion ofdebt contracts renegotiated before maturity. % distressed renegotiations is the percentage of total debtrenegotiations associated with corporate distress. Time to first renegotiation is the average time in yearsto the first renegotiation of contracts that are renegotiated. Effective duration is the mean waiting time tothe first renegotiation or final maturity in years. Effective duration % of stated maturity is the averagetime to the first renegotiation or maturity, expressed in terms of initially stated maturity. Duration% of stated maturity is the average time to any renegotiation or to maturity divided by the initiallystated maturity, including renegotiations occurring after the first renegotiation. Average renegotiationfrequency is the mean number of renegotiation rounds of contracts renegotiated. The last four linessummarize the frequencies of renegotiation rounds. The empirical samples are the loan contract samplesof Denis and Wang (2014), and Roberts and Sufi (2009b). In the simulated samples of the FSI-model,firms only reorganize to avoid default but have an investment option in the spirit of Hackbarth and Mauer(2012). In the simulated samples of the R-model, firms can renegotiate at investment and reorganize toavoid default.

Empirical Empirical Simulated samples Simulated samplesDW 2014 RS 2009b FSI-model R-model

% renegotiated 60.6 64.5 6.3 33.0% distressed renegotiations - 18 100 26.9Time to first renegotiation 1.3 1.5 2.3 1.3Effective duration 2.0 1.5 3.8 2.4Eff. duration % of stated maturity 58 - 97.4 77.8Duration % of stated maturity 61 57 96.2 60.6Average renegotiation frequency 2.7 - 1.33 2.7% renegotiated once 37 - 84.2 43.3% renegotiated twice 22 - 8.7 17.3% renegotiated three times 13 - 3.0 12.0% renegotiated two to five times 53 - 14.4 44.8

entire simulation for the FSI-model, that is, for firms that can renegotiate only in distress.

The third column of Table III summarizes the results for the simulated samples. Only

6.3% of contracts are on average renegotiated. By construction, all renegotiations are due

to corporate distress. The durations are much longer than their empirical counterparts,

and the frequency pattern of the renegotiation rounds per contract fails to reflect that in

the empirical samples. For example, only few contracts are renegotiated more than once.

The final column of Table III shows the renegotiation patterns implied by the R-model

including both distressed reorganization and covenant renegotiation. 33% of contracts

are renegotiated. This number suggests that some renegotiations in the empirical sample

are triggered by motives beyond those reflected in the R-model. We can, however, match

the firm conditions in which renegotiations occur quite well. Specifically, 26.9% of debt

30

renegotiations are distressed reorganizations compared to 18% in the empirical sample of

Roberts and Sufi (2009b). The effective duration is 2.4 years, the average time to first

renegotiation 1.3 years, the effective duration 77.8%, and the duration 60.6%. A compar-

ison of these measures to those in columns one and two shows that the R-model explains

the duration patterns in the empirical sample well. Moreover, the R-model improves the

matching of all empirical timing and duration measures considerably compared to the

FSI-model. We also investigate the renegotiation frequencies in the R-model. 17.3% of

contracts are renegotiated twice and 12% three times. These numbers are much closer to

the empirical fractions of 22% and 13% compared to 8.7% and 3% of the FSI-model.

5.3. Credit spreads

Table IV presents credit spreads in various models. The NRC-model is the model in

Hackbarth and Mauer (2012) with covenant protected debt, in which debt can be rene-

gotiated neither at investment nor in distress. Hence, investment has to be financed with

new equity. We consider the NRC-model to distinguish the impact of the ability to rene-

gotiate from that of having a covenant on credit spreads. For the NRC- and FSI-models,

credit spreads are calculated by first dividing the initial coupon by the initial market

value of debt and then subtracting the risk free interest rate. In the model with both

distressed reorganization and covenant renegotiation (R-Model), the spread between the

debt yield and risk free rate is an insufficient measure of credit risk compensation for

two reasons. First, the initial market value of debt reflects also the present value of the

surplus debt holders obtain at covenant renegotiation. The surplus to debt holders in

renegotiation is defined in Eq. (11). Second, the initial coupon is relatively low because

debt holders anticipate that they obtain part of the renegotiation surplus at covenant

renegotiation. For comparability, we first subtract the present value of the surplus to

debt holders from the initial debt value to obtain the net debt value. Next, we solve for

the fixed coupon over the entire debt maturity that implies the same debt value as the

net debt value. Finally, we calculate credit spreads as this fixed coupon divided by the

initial net debt value and then subtract the risk free interest rate. This credit spread

corresponds to the credit default swap (CDS) spread an external investor would require

to bear the same credit risk as the debt investor in the R-model. The CDS investor would

obtain a constant CDS spread and no surplus at renegotiation. To compare our results

to the observed credit spreads, we use average parameters consistent with Davydenko

31

and Strebulaev (2007), who empirically investigate the determinants of credit spreads as-

sociated with renegotiation.6 Specifically, the market-to-book ratio is 1.86, the leverage

32.2%, the asset volatility 23.9%, and the risk free interest rate 5.93%. The remaining

parameters correspond to those of our baseline firm.

Table IVDebt Renegotiation and Credit Spreads

This table depicts the impact of renegotiable debt on corporate credit spreads. In the first column,we calculate these spreads in a model without any renegotiation (NRC-Model), in which initial debtis covenant protected. The second column uses the distressed reorganization framework of Fan andSundaresan (2000) augmented for investment (FSI-model). The credit spreads in these two models arecalculated by dividing the initial coupon by the market value of debt, and subtracting the risk free interestrate. The third column shows the credit spreads in the model with both distressed reorganization andcovenant renegotiation at investment (R-model). Credit spreads in this model are calculated by firstsubtracting the present value of the surplus from the initial debt market value to obtain the net debtvalue. We then solve for the constant coupon on debt that implies the same value as the net debtvalue. Finally, we calculate the credit spreads by dividing this coupon with the initial net debt value andsubtracting the risk free interest rate. The control premium is the present value of the surplus that debtholders extract at covenant renegotiation, expressed as a percentage of the initial debt value. Baselineparameters are consistent with Davydenko and Strebulaev (2007), given a bargaining power of 0.5.

NRC-model FSI-model R-model Control premium %Baseline parameters 49 214 80 7.88Leverage = 0.372 63 264 98 6.23Volatility σ = 0.289 86 277 117 7.98Market-to-book=1.91 47 221 80 8.14Recovery rate α = 0.65 48 201 76 8.18Bargaining power η = 0.25 49 193 54 12.97Bargaining power η = 0.75 49 250 112 3.46

Column 1 of Table IV shows that the credit spread in the NRC-model is 49 basis points

(bps) in the baseline firm. This credit spread fails to reflect both the mean empirical

spread of 109 bps and the positive dependence of the spread on proxies for bargaining

power reported in Davydenko and Strebulaev (2007).

The R-model reflects three features of empirically observed credit spreads both quali-

tatively and quantitatively: average spread levels, the impact of the possibility to renego-

tiate debt on credit spreads, and cross sectional credit spread patterns. First, Column 3

of Table IV shows that an average baseline firm has a credit spread of 80 bps, which repli-

6While Davydenko and Strebulaev (2007) investigate the credit spreads of corporate bonds, thesespreads also reflect the reduction in agency costs of overleverage and overinvestment when the samefirms have some covenant protected private debt.

32

cates the actually observed mean [median] of 109 [85] bps quite well. The R-model closely

matches the observed credit spreads for a bargaining power of approximately η = 0.72.

Second, a comparison of the R-model to the NRC-model allows us to predict the

impact of the possibility to renegotiate debt on firms. For the baseline firm, the possibility

to renegotiate debt increases the credit spreads by 31 bps (80–49 bps). The empirical

counterpart to a NRC-firm (without the possibility to renegotiate debt) is a firm with

large renegotiation frictions. Davydenko and Strebulaev (2007) use the amount of public

debt as a proxy for renegotiation frictions because it is difficult to renegotiate public

debt in practice. They show that going from the 5th to the 95th percentile of this proxy

increases the credit spreads empirically by 23 bps, which is close to the 31 bps difference

between the NRC- and R-models. Without covenant renegotiation, however, a structural

model cannot replicate this pattern. To confirm this point, we augment the NRC-model

with distressed reorganization. The resulting credit spread of the baseline firm is 50 bps

(not in the table), implying that the possibility to renegotiate in distress increases the

spread by only 1 bps (50–49). The primary reason for the stronger impact of renegotiation

in the R-model is that the renegotiable covenant implies a larger leverage at investment,

which increases the current credit spreads.

Third, the R-model implies a positive dependence of credit spreads on the bargaining

power of equity holders. Column 3 in Table IV shows that an increase from η = 0.25 to

η = 0.75 augments the credit spreads by 58 bps (112–54 bps). The dependence declines

when bankruptcy costs become smaller. With α = 0.8, for example, the credit spreads rise

by only 45 bps when the bargaining power increases from 0.25 to 0.75 (not in the table).

This pattern reflects the empirical relation between bargaining power and credit spreads.

Specifically, Davydenko and Strebulaev (2007) show that credit spreads augment with

proxies for bargaining power and that this dependence declines with proxies for liquidation

costs. In quantitative terms, they illustrate that going from the 5% to the 95% percentiles

of the (significant) bargaining power proxies increases the credit spreads by around 13

bps. The authors, however, argue that the quantitative impact of bargaining power

may actually be higher than their empirical estimate because proxies are noisy measures

of bargaining power. Additionally, they show that the impact of bargaining power is

stronger for firms that can renegotiate debt more easily.

We calculate the credit spreads of the FSI-model in Column 2 of Table IV. This

model neglects the fact that a renegotiable covenant can mitigate agency costs of debt

33

from overleverage at investment and from overinvestment. The FSI-model severely over-

estimates credit spreads by 105 bps (214–109 bps) compared to its empirical counterpart.

Even a considerable variation in bargaining power does not help to drive the spread into

a reasonable range. The FSI-model also predicts a quantitative impact of the possibility

to renegotiate debt that is too large. Specifically, omitting the possibility of distressed

reorganization in the FSI-model leads to the NR-model generating a credit spread of 108

bps. We compare the FSI- and NR-models because both have no covenant thus allowing

us to isolate the pure predicted impact of the ability to renegotiate on credit spreads. The

FSI-model predicts an increases of 106 bps (214–108 bps) in credit spreads, well beyond

the empirical estimation of 23 bps in Davydenko and Strebulaev (2007). Additionally,

Column 2 shows that the FSI-model estimates the impact on credit spreads of a five per-

centage point increase in leverage to 50 bps, in volatility to 63 bps, in market-to-book to

7 bps, and in recovery rate to -13 bps. As illustrated empirically by Davydenko and Stre-

bulaev (2007), a five percentage point increase in these firm characteristics changes the

credit spreads by only 8, 6, 0, and −0.5 bps, respectively. Column 3 shows that incorpo-

rating non-distressed renegotiation in the R-model also helps to mitigate the FSI-model’s

overestimation of the credit spread sensitivities to standard firm parameters.

Overall, we show that incorporating debt renegotiation is important to improve the

ability of structural models to explain both the average and cross section of empirically

observed credit spreads. However, the improvement emerges only if we consider that debt

renegotiation can occur both at distress and outside distress.

The R-model has further implications for debt pricing besides explaining the impact

of debt renegotiation on credit spreads. In particular, the importance of non-distressed

covenant renegotiation for the timing patterns of debt renegotiations described in Section

5.2 and creditors’ ability to extract part of the renegotiation surplus suggest that real

debt prices should reflect a sizeable creditor control premium. Indeed, the recent empirical

study of Feldhutter, Hotchkiss, and Karakas (forthcoming) shows that creditor control

generates a premium in bond prices. The study measures this control premium in the

covenant violation sample of Nini, Smith, and Sufi (2012) by calculating the percentage

premium of public bonds over otherwise identical credit default swap (CDS) implied bond

prices. The resulting average control premium is 1.089%. The R-model’s counterpart to

this premium is the present value of the renegotiation surplus to debt holders, expressed as

a percentage of the initial debt value. The control premium of the R-model is summarized

in the last column of Table IV. Consistent with Feldhutter, Hotchkiss, and Karakas

34

(forthcoming), the R-model’s premium spikes around covenant renegotiation events upon

which control rights are shifted to creditors (not in the table) and increases with the

recovery rate. A novel prediction is that the control premium should be larger for firms

with a higher market-to-book ratio. We also predict a larger size for the control premium

than that in the study of Feldhutter, Hotchkiss, and Karakas (forthcoming) for two

reasons. First, the latter measures the premium of public bonds, whereas we model the

premium of private debt that is easier for creditors to renegotiate. Second, the bonds in

Feldhutter, Hotchkiss, and Karakas (forthcoming) do not coincide with the bank loans

in Nini, Smith, and Sufi (2012) for which a covenant is actually violated and, hence,

need to be renegotiated. Feldhutter, Hotchkiss, and Karakas (forthcoming) argue that

such bonds can still indirectly profit from a general corporate restructuring involving

all creditors after a violation. For the private loans that we model, however, creditors

directly renegotiate the terms of their contract with the firm. In the base case, the R-

model’s control premium is 7.88%. This premium strongly depends on bargaining power.

With η = 0.75, for example, the control premium is only 3.46%.

5.4. Covenant structures

Section 4.2 shows that including a renegotiable financing covenant increases firm value.

However, in the NR-model without renegotiation, we find that a financing covenant re-

duces the baseline firm value from 66.49 to 64.84 due to reduction in the firm’s financial

flexibility to upstructure capital. These results are consistent with the empirical obser-

vation that financing covenants are ubiquitous in debt contracts (Bradley and Roberts,

2015) and private debt is more likely to have restrictive covenants than public bonds

(Kahan and Tuckman, 1993; Kwan and Carleton, 2010). We also derive cross sectional

predictions in terms of firms’ incentives to install a financing covenant in private debt.

Specifically, the firm value differences between the FSI- and R-models in Table I of Section

4.2 imply that firms with higher bargaining power, larger growth opportunities, higher

tax rate, lower recovery rate, smaller volatility, and lower cash flow drift should have a

weaker incentive to implement a financing covenant.

Our cross sectional results are consistent with the empirical results in Bradley and

Roberts (2015) that private debt covenants are more likely for higher cash flow volatility.

However, according to the same study, high market-to-book firms have a larger propensity

toward private debt covenants. Demiroglu and James (2010) relativize this empirical

35

result by showing that banks include more but looser financial covenants in loans of

growth firms.

5.5. Financial and investment policies

Figure 4 plots the optimal initial leverage of a baseline firm with a renegotiable financing

covenant (solid line) and that of a FSI-model firm (dashed line) against the bargaining

power of equity holders.

INSERT FIGURE 4 HERE

As covenant renegotiation reduces the agency costs of debt, the optimal initial leverage

of the baseline firm with renegotiation is larger than that of the FSI-model firm. This

difference is particularly pronounced for a lower η primarily because the net benefit of a

financing covenant declines with bargaining power (see Section 4.2). The analysis implies

that the choice of capital structure strongly depends on whether a financing covenant is

included. A novel empirical prediction is that the impact of covenants on capital structure

should be particularly pronounced for firms in which equity holders have weak bargaining

power. Additionally, we predict that bargaining power is more important to the leverage

choice of firms with a financing covenant.

Figure 5 plots the market-to-book ratio against optimal leverage for the R-model

(solid line), FSI-model (dashed line), NRC-model with a covenant (dashed-dotted line),

and NR-model without a covenant (dotted line). In the R- and FSI-models, we set

η = 0.5. Billett, King, and Mauer (2007) find that the covenant protection of public

bonds reduces the negative relation between leverage and growth opportunities. The

dashed-dotted and dotted lines are consistent with this empirical finding. The agency

costs of debt increase with the importance of the investment opportunity, thus explaining

the decline of the dotted line in the NR-model. As a covenant mitigates the agency costs

of debt, the decline of the dashed-dotted line in the NRC-model is less pronounced. With

distressed reorganization, debt becomes riskier, thus raising the agency costs of debt.

Therefore, the difference in the decline between the dashed and solid lines of the models

with debt renegotiation is more pronounced than that between the dotted and dashed-

dotted lines. A novel prediction of this comparison is that the covenant protection of

36

renegotiable private debt should reduce the negative relation between leverage and growth

opportunities more than the covenant protection of public debt.

INSERT FIGURE 5 HERE

In Figure 6, we investigate the impact of covenants and bargaining power on invest-

ment timing in the baseline firm. The solid line depicts the optimal investment threshold

of the R-model and the dashed line that of the FSI-model firm. Both lines are plotted

for an optimal initial coupon.

INSERT FIGURE 6 HERE

A comparison of the solid and the dashed lines yields the empirical prediction that

installing a financing covenant delays investment. The reason is that equity holders

obtain a lower surplus at investment and cannot expropriate debt holders in the R-model

compared to the FSI-model. We also find that this investment delay should be more

distinct for low levels of η for which the surplus reduction is particularly pronounced and

the initial leverage is larger, thus increasing the wealth expropriation at investment in

the FSI-model.7

6. Conclusion

Existing corporate finance models cannot explain the quantitative impact of the possi-

bility to renegotiate debt on the value of corporate securities. We argue that this gap is

due to the lack of these models’ ability to reflect that debt renegotiations generally occur

very frequently and, specifically, mostly arise outside distress (see, e.g., Roberts and

Sufi, 2009b). In this paper, we develop a model in which equity holders can renegotiate

debt with creditors either upon investment to waive a financing covenant or at corporate

distress to reorganize the capital structure. Renegotiation at investment mitigates the

agency costs of debt and distressed reorganization avoids the expected bankruptcy costs.

We find that incorporating renegotiation both outside and in corporate distress is crucial

to explain the empirically observed patterns of the timing of debt renegotiation.

7Both empirical predictions hold with a fixed instead of optimal initial coupon.

37

A model capturing a realistic timing of debt renegotiations provides a fundamental

step towards understanding the quantitative impact of creditors through the possibility

of renegotiating their claims on firms. The presented model explains a rich set of cross

sectional empirical results in terms of the impact of firm characteristics on credit spreads,

covenant structures, and corporate financial policies. A key insight is that a model

capturing the timing patterns of renegotiations implies a first order effect of creditor

governance on firm value. Further, the bargaining power of equity holders and creditors

is a quantitatively important determinant of firm policies and of the value of corporate

securities. A recent literature investigates the impact of creditor rights on the access

to finance, leverage, investment, risk taking, and demand for debt of distressed firms

(Porta, Lopez-de-Silanes, and Shleifer, 2008; Acharya, Sundaram, and John, 2011; Vig,

2013; Favara, Morellec, Schroth, and Valta, forthcoming). Our results on the importance

of covenant renegotiation motivate the consideration of creditor rights also in future

empirical studies of non-distressed firms. To stimulate further research in this direction,

we generate several novel testable predictions on the impact of bargaining power on

corporations. We also suggest that private debt should entail a sizeable control premium

beyond that observed in public bonds, and that this premium should strongly depend on

bargaining power. This hypothesis has not been explored in the empirical literature.

We only analyze the renegotiation of a financing covenant. Considering alternative

covenants could generate supplementary insights on the impact of creditor governance on

firms. We also believe that non-distressed covenant renegotiation should help rationalize

observed corporate debt structures, such as the choice between private and public debt

or firms’ debt ownership structure. We look forward to future research addressing these

extensions.

38

References

Acharya, V. V., R. K. Sundaram, and K. John (2011): “Cross-country variations

in capital structures: The role of bankruptcy codes,” Journal of Financial Intermedi-

ation, 20, 25–54.

Almeida, H. and T. Philippon (2007): “The risk-adjusted cost of financial distress,”

Journal of Finance, 62, 2557–2586.

Anderson, R. W. and S. Sundaresan (1996): “The design and valuation of debt

contracts,” Review of Financial Studies, 9, 37–68.

Arnold, M., A. F. Wagner, and R. Westermann (2013): “Growth options,

macroeconomic conditions, and the cross-section of credit risk,” Journal of Financial

Economics, 107, 350–385.

Bergman, Y. and J. Callen (1991): “Opportunistic underinvestment in debt rene-

gotiation and capital structure,” Journal of Financial Economics, 29, 137–171.

Berlin, M. and L. Mester (1992): “Debt covenants and renegotiation,” Journal of

Financial Intermediation, 2, 95–133.

Bhamra, H. S., L.-A. Kuehn, and I. A. Strebulaev (2010): “The levered equity

risk premium and credit spreads: A unified framework,” Review of Financial Studies,

23, 645–703.

Bhattacharya, S. and A. Faure-Grimaud (2001): “The debt hangover renegotia-

tion with noncontractible investment,” Economics Letters, 70, 413–419.

Billett, M. T., T.-H. D. King, and D. C. Mauer (2007): “Growth opportunities

and the choice of leverage, debt maturity, and covenants,” Journal of Finance, 62,

697—730.

Bolton, P. and D. Scharfstein (1996): “Debt structure and the number of credi-

tors,” Journal of Political Economy, 104, 1–25.

Bradley, M. and M. R. Roberts (2015): “The structure and pricing of corporate

debt covenants,” Quarterly Journal of Finance, 5.

Chava, S. and M. R. Roberts (2008): “How does financing impact investment? The

role of debt covenant violations,” Journal of Finance, 63, 2085–2121.

39

Chen, H. (2010): “Macroeconomic conditions and the puzzles of credit spreads and

capital structure,” Journal of Finance, 65, 2171–2212.

Chen, L., P. Collin-Dufresne, and R. S. Goldstein (2009): “On the relation

between the credit spread puzzle and the equity premium puzzle,” Review of Financial

Studies, 22, 3367–3409.

Childs, P. D., D. C. Mauer, and S. H. Ott (2005): “Interactions of corporate fi-

nancing and investment decisions: The effects of agency conflicts,” Journal of Financial

Economics, 76, 667–690.

Christensen, P. O., C. R. Flor, and K. R. Miltersen (2014): “Dynamic capital

structure with callable debt and debt renegotiations,” Journal of Corporate Finance,

29, 644–661.

Datta, S., M. Datta-Iskandar, and A. Patel (1999): “Bank monitoring and the

pricing of corporate public debt,” Journal of Financial Economics, 51, 435–449.

Davydenko, S. A. and I. A. Strebulaev (2007): “Strategic actions and credit

spreads: An empirical investigation,” Journal of Finance, 62, 2633–2671.

Demiroglu, C. and C. M. James (2010): “The information content of bank loan

covenants,” Review of Financial Studies, 23, 3700–3737.

Denis, D. J. and V. T. Mihov (2003): “The choice among bank debt, non-bank

private debt, and public debt: Evidence from new corporate borrowings,” Journal of

Financial Economics, 70, 3–28.

Denis, D. J. and J. Wang (2014): “Debt covenant renegotiations and creditor control

rights,” Journal of Financial Economics, 113, 348–367.

Dessein, W. (2005): “Information and control in ventures and alliances,” Journal of

Finance, 60, 2513–2549.

Dichev, I. and D. Skinner (2002): “Large-sample evidence on debt covenant hypoth-

esis,” Journal of Accounting Research, 4, 1091–1123.

Dudley, E. (2012): “Capital structure and large inestment projects,” Journal of Cor-

porate Finance, 18, 1168–1192.

40

Eom, Y. H., J. Helwege, and J.-Z. Huang (2004): “Structural models of corporate

bond pricing: An empirical analysis,” Review of Financial Studies, 17, 498–544.

Fan, H. and S. M. Sundaresan (2000): “Debt valuation, renegotiation, and optimal

dividend policy,” The Review of Financial Studies, 13, 1057–1099.

Favara, G., E. Morellec, E. Schroth, and P. Valta (forthcoming): “Debt en-

forcement, investment, and risk taking across countries,” Journal of Financial Eco-

nomics.

Feldhutter, P., E. Hotchkiss, and O. Karakas (forthcoming): “The value of

creditor control in corporate bonds,” Journal of Financial Economics.

Gamba, A. and A. Triantis (2014): “How effectively can debt covenants alleviate

financial agency problems,” Unpublished Working Paper.

Garleanu, N. and J. Zwiebel (2009): “Design and renegotiation of debt covenants,”

Review of Financial Studies, 22, 749–781.

Giammarino, R. (1989): “The resolution of financial distress,” Review of Financial

Studies, 2, 25–47.

Gopalakrishnan, G. and M. Parkash (1995): “Borrower and lender perceptions

of accounting information in corporate lending agreements,” Accounting Horizons, 9,

13–26.

Gorton, G. and J. Kahn (2000): “The design of bank loan contracts,” Review of

Financial Studies, 13, 331–364.

Grossman, S. and O. Hart (1986): “The costs and benefits of ownership: A theory

of vertical and lateral integration,” Journal of Political Economy, 94, 691–719.

Hackbarth, D. and D. C. Mauer (2012): “Optimal priority structure, capital struc-

ture, and investment,” The Review of Financial Studies, 25, 747–796.

Hackbarth, D., J. Miao, and E. Morellec (2006): “Capital structure, credit risk,

and macroeconomic conditions,” Journal of Financial Economics, 82, 519–550.

He, Z. and W. Xiong (2012): “Rollover risk and credit risk,” Journal of Finance, 67,

391—429.

41

Hennessy, C. A. (2004): “Tobin’s Q, debt overhang and investment,” Journal of Fi-

nance, 59, 1717–17472.

Huang, J.-Z. and M. Huang (2012): “How much of the corporate-treasury yield

spread is due to credit risk? A new calibration approach,” Review of Asset Pricing

Studies, 2, 153–202.

Hugonnier, J., S. Malamud, and E. Morellec (2015): “Capital supply uncer-

tainty, cash holdings, and investment,” Review of Financial Studies, 28, 391–445.

Kahan, M. and E. Rock (2009): “Hedge fund activism in the enforcement of bond-

holder rights,” Northwestern University Law Review, 103, 282–322.

Kahan, M. and B. Tuckman (1993): “Private vs. public lending: Evidence from

covenants,” Unpublished Working Paper.

Krishnaswami, S., P. A. Spindt, and V. Subramaniam (1999): “Information

asymmetry, monitoring, and the placement structure of corporate debt,” Journal of

Financial Economics, 51, 407–434.

Kwan, S. H. and W. T. Carleton (2010): “Financial contracting and the choice

between private placement and publicly offered bonds,” Journal of Money, Credit and

Banking, 42, 907–929.

Leland, H. E. (1998): “Agency costs, risk management, and capital structure,” Journal

of Finance, 53, 1213–1243.

Lin, C., Y. Ma, P. Malatesta, and Y. Xuan (2011): “Ownership structure and

the cost of corporate borrowing,” Journal of Financial Economics, 100, 1–23.

Mella-Barral, P. (1999): “The dynamics of default and debt reorganization,” Review

of Financial Studies, 12, 535–578.

Mella-Barral, P. and W. Perraudin (1997): “Strategic debt service,” Journal of

Finance, 52, 531–556.

Mello, A. and J. Parsons (1992): “Measuring the agency cost of debt,” Journal of

Finance, 47, 1887–1904.

Nini, G., D. C. Smith, and A. Sufi (2009): “Creditor control rights and firm invest-

ment policy,” Journal of Financial Economics, 92, 400–420.

42

——— (2012): “Creditor control rights, corporate governance, and firm value,” Review

of Financial Studies, 25, 1713–1761.

Porta, R. L., F. Lopez-de-Silanes, and A. Shleifer (2008): “The economic

consequences of legal origins,” Journal of Economic Literature, 46, 285–332.

Rajan, R. G. (1992): “Insiders and outsiders: The choice between informed and arm’s-

length debt,” Journal of Finance, 47, 1367–1400.

Roberts, M. R. (2015): “The role of dynamic renegotiation and asymmetric informa-

tion in financial contracting,” Journal of Financial Economics, 116, 61–81.

Roberts, M. R. and A. Sufi (2009a): “Control rights and capital structure: An

empirical investigation,” Journal of Finance, 64, 1657–1695.

——— (2009b): “Renegotiation of financial contracts: Evidence from private credit agree-

ments,” Journal of Financial Economics, 93, 159–184.

Smith, Jr. , C. W. and J. B. Warner (1979): “On financial contracting: An analysis

of bond covenants,” Journal of Financial Economics, 7, 117–161.

Strebulaev, I. A. (2007): “Do tests of capital structure theory mean what they say?”

Journal of Finance, 62, 1747–1787.

Sundaresan, S. and N. Wang (2007): “Investment under uncertainty with strategic

debt service,” American Economic Review, 97, 256–261.

Vig, V. (2013): “Access to collateral and corporate debt structure: Evidence from a

natural experiment,” Journal of Finance, 68, 881–927.

Wang, J. (2013): “Debt covenant design and creditor control rights: Evidence from

covenant restrictiveness and loan outcomes,” Unpublished Working Paper.

Whited, T. M. (1992): “Debt, liquidity constraints, and corporate investment: Evi-

dence from panel data,” Journal of Finance, 47, 1425–1460.

Zhang, B. Y., H. Zhou, and H. Zhu (2009): “Explaining credit default swap spreads

with the equity volatility and jump risks of individual firms,” Review of Financial

Studies, 22, 5099–5131.

43

Figures

Fir

min

itia

tion

(t=

0)

Init

ial

reor

ganiz

atio

n(S

0)

Inve

stm

ent

afte

rin

itia

lre

orga

niz

atio

n(U

1)

Reo

rgan

izat

ion

afte

rin

vest

men

tfo

llow

ing

reor

ganiz

atio

n(S

2)

sub

scri

pt

3

sub

scri

pt

2

sub

scri

pt

1l

sub

scri

pt

0

Cov

enan

tre

neg

otia

tion

atin

vest

men

t(U

0)

Reo

rgan

izat

ion

afte

rin

vest

men

t(S

1)

sub

scri

pt

2

sub

scri

pt

1h

sub

scri

pt

0

Fig

ure

1.

Tim

elin

eof

the

pote

nti

al

occ

urr

ence

of

debt

renegoti

ati

on.

This

figu

resh

ows

the

sequen

ceof

the

pot

enti

alocc

urr

ence

ofco

venan

tre

neg

otia

tion

,dis

tres

sed

reor

ganiz

atio

n,

and

inve

stm

ent

over

tim

e.T

he

not

atio

nfo

rth

eco

rres

pon

din

gth

resh

olds

are

inpar

enth

esis

.T

he

subsc

ripts

apply

toth

eco

rres

pon

din

gva

lue

funct

ions.

44

Market-to-Book Ratio1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

Expe

cted

Yea

rs u

ntil

Ren

egot

iatio

n

0

1

2

3

4

5

6

7

Figure 2. Expected waiting time to renegotiation. This figure plots the relationbetween the market-to-book ratio of a R-model firm and the expected waiting time toany renegotiation.

Market-to-Book ratio1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

Prob

(Cov

enan

t Ren

egot

iatio

n)

0

0.2

0.4

0.6

0.8

1

Figure 3. Probability of covenant renegotiation conditional on any renegotia-tion. This figure shows the relation between the market-to-book ratio of a R-model firmand the probability of covenant renegotiation given any renegotiation occurs.

45

Bargaining Power0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Leve

rage

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Figure 4. Optimal initial leverage choice. This figure shows the relation betweenoptimal initial leverage and bargaining power of equity holders for the R-model firm (solidline) and for the FSI-model firm (dashed line).

Market-to-Book Ratio1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85

Leve

rage

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

Figure 5. Relation between market-to-book ratio and leverage. This figureplots the relation between market-to-book and market leverage for a baseline firm in theR-model (solid line) and in the FSI-model (dashed line). The dashed-dotted line plotsthis relation for a NR-model firm without renegotiation and the dotted line that for aNRC-model firm without renegotiation but with a financing covenant.

46

Bargaining Power0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Inve

stm

ent T

hres

hold

1.6

1.8

2

2.2

2.4

2.6

2.8

Figure 6. Investment timing. This figure shows the relation between the optimalinvestment threshold and bargaining power of equity holders in the R-model (solid line)and in the FSI-model (dashed line). We use the optimal initial coupon for each firm.

Appendix

A. Initial reorganization, value functions thereafter

S0 and U0 denote the initial reorganization and investment boundary, respectively. Define

Sν0 as the first time the firm reaches the initial reorganization threshold, i.e.,

Sν0 := inf {t ≥ 0 : Xt ≤ S0 |X0 = X } , (39)

and let Uν0 denote the first time it reaches the investment threshold, i.e.,

Uν0 := inf {t ≥ 0 : Xt ≥ U0 |X0 = X } . (40)

T0 is the first time the firm reaches initial reorganization or investment, i.e.,

T0 := inf {Sν0 , Uν0 } . (41)

47

This Appendix A considers the case in which T0 = Sν0 , i.e., reorganization occurs before

investment.

The value functions and corporate policies after investment following initial reorgani-

zation are analogous to the case derived in Fan and Sundaresan (2000). We also present

them for the sake of completeness.

Unlevered firm value. The unlevered firm value after the second (final) reorganization,

v3 (X) , corresponds to

v3 (X) =1− τr − µ

X. (42)

The valuation of equity after investment following initial reorganization. The value of

equity after investment following initial reorganization, denoted by e2 (X) , corresponds

to the present value of the expected payoffs to shareholders until reorganization plus the

payoff at reorganization, i.e.,

e2 (X) = EQ[∫ Sν2

t

e−r(u−t) (1− τ) (Xu − c2) du+ e−rSν2 θ2v3 (S2) |Xt = X

], (43)

in which Sν2 is the first time the firm reaches the reorganization threshold after investment

following reorganization, i.e.,

Sν2 = inf {t ≥ T0 : Xt ≤ S2 |T0 = Sν0 } , (44)

and S2 is the firm’s reorganization threshold after investment following initial reorgani-

zation. c2 is the coupon of the firm after investment following reorganization. Solving

the corresponding Hamilton-Jacobi-Belman equation yields

e2 (X) = Ae20 + Ae21 X + Ae22 Xβ2 , (45)

in which

β2 =1

2− µ

σ2−

√(1

2− µ

σ2

)2

+2r

σ2, (46)

Ae20 = −1− τr

c2, Ae21 =1− τr − µ

, (47)

Ae22 =

(r − µr

)1−β2 ( β2β2 − 1

)−β2c1−β22

1− τr − µ

(1− θ2)1−β21

1− β2. (48)

48

The optimal reorganization threshold after investment following initial reorganization is

calculated as

S2 =β2

β2 − 1

r − µr

1

1− θ2c2. (49)

The valuation of corporate debt after investment following initial reorganization. Sim-

ilarly, the value of total corporate debt after investment following initial reorganization,

denoted by d2 (X) , corresponds to the present value of the expected payoffs to debt

holders until reorganization plus the payoff at reorganization, i.e.,

d2 (X) = EQ[∫ Sν2

t

e−r(u−t)c2du+ e−rSν2 (1− θ2) v3 (S2) |Xt = X

]. (50)

Solving the associated Hamilton-Jacobi-Belman equation, we find that

d2 (X) = Ad20 + Ad22 Xβ2 , (51)

in which

Ad20 =c2r

(52)

Ad22 =

(r − µr

)−β2 ( β2β2 − 1

)−β2c1−β22

1

r

(1

1− θ2

)1−β2 ((1− τ)

β2β2 − 1

− 1

), (53)

and β2 is defined in Eq. (46).

Capital structure at investment after initial reorganization. The threshold for invest-

ment after initial reorganization is denoted by U1. At investment after reorganization,

equity holders choose the first-best capital structure. The reason is that the firm is an all

equity financed firm after initial reorganization and the issue proceeds of new debt accrue

to equity holders. The optimal (first-best) capital structure is obtained by maximizing

firm value, which yields the coupon

c2 = cfb2 =r

r − µβ2 − 1

β2(1− β2)

1β2 (1− θ2)U1. (54)

We calculate the corresponding first-best firm value as

f2 (U1) = f fb2 (U1) =[1− τ + τ (1− β2)

1β2 (1− θ2)

] U1

r − µ. (55)

49

The firm value can be decomposed into the unlevered asset value and the value of the tax

shield, in which the latter also incorporates the loss of tax shield due to the debt-equity-

swap in case of final reorganization.

The valuation of equity after initial reorganization. The value of equity after initial

reorganization, denoted by e1l (X) , corresponds to the present value of the expected pay-

offs to shareholders until investment plus the expected value of the payoff at investment,

i.e.,

e1l (X) = EQ[∫ Uν1

t

e−r(u−t) (1− τ)Xudu+ e−rUν1 (f2 (sU2)− I) |Xt = X

], (56)

in which Uν1 is the first time the firm reaches the investment threshold after initial reor-

ganization, i.e.,

Sν2 = inf {t ≥ T0 : Xt ≥ U1 |T0 = Sν0 } , (57)

and U1 is the firm’s investment threshold after initial reorganization. f2 (·) is the firm

value after investment following initial reorganization as given in closed-form by Eq. (55).

Solving the corresponding Hamilton-Jacobi-Belman equation yields

e1l (X) = Ae1l1 X + Ae1l2 Xβ1 , (58)

in which

β1 =1

2− µ

σ2+

√(1

2− µ

σ2

)2

+2r

σ2, Ae1l1 =

1− τr − µ

(59)

Ae1l2 =

(β1

β1 − 1

)−β1 ( I (r − µ)

(s− 1) (1− τ) + sτ (1− β2)1β2 (1− θ2)

)−β1I

β1 − 1. (60)

Initial reorganization. The initial reorganization problem reads

θ0 = arg maxθ0

{θ0e1l (S0)− 0

}η {(1− θ0

)e1l (S0)− α

1− τr − µ

S0

}1−η

. (61)

This problem is equivalent to

θ0 = arg maxθ0

η log{θ0e1l (S0)

}+ (1− η) log

{(1− θ0

)e1l (S0)− α

1− τr − µ

S0

}. (62)

50

The first order condition with respect to θ0 is

0 = ηe1l (S0)

θ0e1l (S0)+ (1− η)

−e1l (S0)

(1− θ0) e1l (S0)− αv1 (S0). (63)

Define the surplus of initial reorganization to equity holders, debt holders, and total, as

SE (S0) = θ0e1l (S0) (64)

SD (S0) = (1− θ0) e1l (S0)− αv1 (S0) (65)

ST (S0) = e1l (S0)− αv1 (S0) , (66)

respectively. Plugging these definitions into Eq. (63) and solving yields

SE (S0) = ηST (S0) (67)

SD (S0) = (1− η)ST (S0) , (68)

which shows that the surplus of renegotiation is apportioned such that each party receives

a fraction of total surplus corresponding to its respective bargaining power. Finally, Eq.

(67) implies the solution as stated in Eq. (8) of Section 3.1:

θ0 = η

(1− α v2 (S0)

e1l (S0)

). (69)

B. Value functions after covenant renegotiation at in-

vestment

We now consider the case in which T0 = Uν0 , i.e., investment takes place before initial

reorganization. The value of equity after covenant renegotiation at investment, e1h (X),

is analogous to the case after investment following initial reorganization (Eqs. (45)-(48)).

The reorganization threshold after covenant renegotiation at investment exhibits the same

functional form as the reorganization threshold after investment following initial reorga-

nization (Eq. (49)):

S1 =β2

β2 − 1

r − µr

1

1− θ1(cA01 + cB1

). (70)

The value function of total corporate debt is analogous to the value function of corporate

debt after investment following initial reorganization (Eqs. (51)- (53)).

51

The value function of corporate debt of initial debt holders, who have a claim on the

coupon cA01, is given by:

d1h(X; cA01

)= A

dA1h0 + A

dA1h2 Xβ2 , (71)

in which

AdA1h0 =

cA01r

(72)

AdA1h2 =

(β2 (r − µ)

(β2 − 1) r

)−β2 1

rcA01 (c1)

−β2(

1

1− θ1

)1−β2 ((1− τ)

β2β2 − 1

− 1

). (73)

Analogously, the value function of corporate debt of new debt holders, who have a claim

on the coupon cB1 = c1 − cA01, can be written as:

d1h(X; cB1

)= A

dB1h0 + A

dB1h2 Xβ2 , (74)

in which

AdB1h0 =

cB01r

(75)

AdB1h2 =

(β2 (r − µ)

(β2 − 1) r

)−β2 1

rcB1 (c1)

−β2(

1

1− θ1

)1−β2 ((1− τ)

β2β2 − 1

− 1

). (76)

C. Covenant renegotiation

Proof of Proposition 1. The covenant renegotiation problem is stated in Eq. (12), Section

3.3 of the main text. A change of variables yields

max{cA01,cB1 }

(e1h(sU0; c

A01 + cB1

)+ d1h

(sU0; c

B1

)− e1h

(sU0; c

A0

))η·(d1h(sU0; c

A01

)− d1h

(sU0; c

A0

))1−η= max{cA01,c1}

(e1h (sU0; c1) + d1h

(sU0; c1 − cA01

)− e1h

(sU0; c

A0

))η·(d1h(sU0; c

A01

)− d1h

(sU0; c

A0

))1−η= max

{c1}

[max{cA01}

(e1h (sU0; c1) + d1h

(sU0; c1 − cA01

)− e1h

(sU0; c

A0

))η·(d1h(sU0; c

A01

)− d1h

(sU0; c

A0

))1−η]. (77)

52

The last equality uses the fact that c1 is bounded by the firm’s debt capacity from above

and by zero from below; cA01 is bounded by c1 above and by zero from below. Hence,

the range of{cA01, c1

}is a convex and compact set in R2. Note that this property also

guarantees the existence of the maximum. Therefore, we proceed by solving the following

problem for an arbitrary, but fixed, c1 :

{cA01}

= arg max{cA01}

(e1h (sU0; c1) + d1h

(sU0; c1 − cA01

)− e1h

(sU0; c

A0

))η·(d1h(sU0; c

A01

)− d1h

(sU0; c

A0

))1−η. (78)

Recall that total surplus from covenant renegotiation is calculated as

ST(U0; c

A01, c1

)= f1h (sU0; c1)− e1h

(sU0; c

A0

)− d1h

(sU0; c

A0

), (79)

cf. Eq. (15). In particular, for any given total coupon c1, total firm value and total surplus

are independent of the coupon to initial debt holders cA01, such that we can write

ST(U0; c

A01, c1

)= ST (U0; c1) . (80)

Intuitively, firm value is determined by the total coupon, but not by the allocation of

the total coupon to new and existing debt holders. Hence, re-writing Eq. (78), using this

insight and the definition of total surplus in Eq. (13), yields that for any given c1, cA01 is

the solution to the maximization problem

{cA01}

= arg max{cA01}

(SE

(U0; c

A01, c1

))η (ST (U0; c1)− SE

(U0; c

A01, c1

))1−η. (81)

The first order condition with respect to cA01 reads:

η

∂∂cA01

SE(U0; c

A01, c1

)SE (U0; cA01, c1)

+ (1− η)− ∂∂cA01

SE(U0; c

A01, c1

)ST (U0; c1)− SE (U0; cA01, c1)

= 0, (82)

which is equivalent to

SE(U0; c

A01, c1

)= ηST (U0; c1) . (83)

Consequently,

SD(U0; c

A01, c1

)= (1− η)ST (U0; c1) , (84)

53

which completes the proof of (ii). Intuitively, the surplus to equity holders is a fraction

η of total surplus, in which η corresponds to equity holders’ bargaining power. In turn,

the surplus to debt holders is a fraction 1− η of total surplus, in which 1− η corresponds

to debt holders’ bargaining power.

To prove (i), consider the maximization problem

{c1} = arg max{c1}

(SE

(U0; c

A01, c1

))η (ST (U0; c1)− SE

(U0; c

A01, c1

))1−η= arg max

{c1}(ηST (U0; c1))

η ((1− η)ST (U0; c1))1−η , (85)

in which we use Eqs. (83) and (84). Then, the first order condition with respect to c1 is

given by:

ηη ∂∂c1ST (U0; c1)

ηST (U0; c1)+ (1− η)

(1− η) ∂∂c1ST (U0; c1)

(1− η)ST (U0; c1)= 0, (86)

which is equivalent to∂

∂c1ST (U0; c1) = 0, (87)

which proves part (i) using concavity of the total surplus. In words, the total new coupon

from renegotiation is determined such that total surplus is maximized. Because total

surplus is maximized at the optimal first-best capital structure at U0, the total coupon

is given by

c1 = cfb1 =r

r − µβ2 − 1

β2(1− β2)

1β2 (1− θ)U0, (88)

analogous to Appendix A, Eq. (54). Hence,

cB1 + cA01 = cfb1 . (89)

The corresponding first-best firm value at U0 is analogous to Eq. (55) of Appendix A:

f1 (U0) = f fb1 =[1− τ + τ (1− β2)

1β2 (1− θ)

] U0

r − µ(90)

54

D. Value functions and corporate policies before rene-

gotiation at investment or initial reorganization

The valuation of equity. The value of equity before investment or initial reorganization,

e0 (X) , corresponds to the present value of expected future cash flows to equity holders,

i.e.,

e0 (X) = EQ[∫ T0

t

e−r(u−t) (1− τ)(Xu − cA0

)du |Xt = X

]+EQ

[1T0=Sν0 e

−r(Sν0−t)θ0e1l (S0) |Xt = X]

(91)

+EQ[1T0=Uν0 e

−r(Uν0−t)(e1h (sU0; c1)−

(I − d1h

(sX; cB1

)))|Xt = X

],

in which Sν0 , Uν0 , and T0 are defined in Eqs. (39)-(41), and cA01 and cn are determined

by Eq. (12). The first line of Eq. (91) corresponds to the cash flow to equity holders

until initial reorganization or covenant renegotiation at investment. In case of distressed

reorganization, equity holders obtain a fraction θ0 of the unlevered firm value (second

line). The third line shows the value of equity at covenant renegotiation. The associated

ordinary differential equation (ODE) readse0 (X) = θ0e1l (X) 0 ≤ X ≤ S0

re0 (X) = (1− τ)(X − cA0

)+ µXe′0 (X) + 1

2σ2X2e′′0 (X) S0 < X < U0

e0 (X) = e1h(sX; cA01 + cB1

)−(I − d1h

(sX; cB1

))X ≥ U0,

(92)

subject to the boundary conditions

e0 (S0) = θ0e1l (S0) (93)

e0 (U0) = e1h (sU0; c1)−(I − d1h

(sU0; c

B1

)). (94)

Standard arguments and plugging Eqs. (18) and (19) into Eq. (94) imply the solution as

stated in the main text of Section 3.4, Eqs. (21)–(27).

55

The valuation of corporate debt. The value of debt before investment or initial reorga-

nization, d0 (X) , corresponds to the present value of expected future cash flows to debt

holders, i.e.,

d (X) = EQ[∫ T0

t

e−r(u−t)cA0 du |Xt = X

]+ EQ [1T0=Uν0 d1h (sU0; c

A01

)].

+EQ[1T0=Sν0 e

−r(Sν0−t) (1− θ0) e1l (XS) |Xt = X]

(95)

The first term in the first line of Eq. (95) shows the value of coupon payments to debt

holders until covenant renegotiation at investment or initial reorganization. In case of

covenant renegotiation at investment, initial debt holders have a claim on the total coupon

cA01 determined by the Nash solution, which corresponds to the second term in the first

line of Eq. (95). In case of reorganization, debt holders receive a fraction (1− θ0) of the

unlevered equity value, line two of Eq. (95). The ODE for the value of debt is given byd0 (X) = (1− θ0) e1l (X) 0 ≤ X ≤ S0

rd0 (X) = cA0 + µXd′0 (X) + 12σ2X2d′′0 (X) S0 < X < U0

d0 (X) = d1h(sX; cA01

)X ≥ U0,

(96)

subject to the boundary conditions

d0 (S0) = (1− θ0) e1l (XS) , d0 (U0) = d1h(sX; cA01

). (97)

Standard arguments and plugging Eqs. (18) and (20) into Eq. (97) imply the solution as

stated in the main text of Section 3.4, Eqs. (28)–(32).

E. FSI-model

The FSI-model corresponds to the model of Fan and Sundaresan (2000), augmented with

lumpy investment as in Hackbarth and Mauer (2012).

There is no covenant after initial reorganization because the firm is all equity financed

up to investment. Hence, the value functions and boundaries e1l (X) , e2 (X) , d2 (X) ,

v3 (X) , U1, and S2 are calculated with the same formulas as in the R-Model.

56

Similarly, the formulas for reorganization after covenant renegotiation remain un-

changed (e1h (X), total debt d1h (X), and S1).

We now derive the value functions before investment or initial reorganization. At the

investment boundary U0, equity holders determine the coupon of new debt by maximizing

the value of equity and new debt:

cB1 = arg maxcB1

e1h(sU0; c

A0 + cB1

)+ d1h

(sU0; c

B1

)(98)

The resulting coupon cB1 corresponds to second-best financing of the investment opportu-

nity because equity holders do not incorporate the dilution of initial debt holders’ claim.

Hence, equity holders overlever, i.e., the resulting total coupon c1 = cA0 +cB1 is larger than

the first-best coupon (Hackbarth and Mauer, 2012). The value of initial debt incorporates

this potential dilution of the debt claim at investment.

This financing choice affects the boundary condition in the ordinary differential equa-

tion (ODE) that determines the value of equity:e0 (X) = θ0e1l (X) 0 ≤ X ≤ S0

re0 (X) = (1− τ)(X − cA0

)+ µXe′0 (X) + 1

2σ2X2e′′0 (X) S0 < X < U0

e0 (X) = e1h(sX; cA0 + cB1

)−(I − d1h

(sX; cB1

))X ≥ U0,

(99)

subject to the boundary conditions

e0 (S0) = θ0e1l (S0) (100)

e0 (U0) = e1h (sU0; c1)−(I − d1h

(sU0; c

B1

)), (101)

in which cB1 is determined by Eq. (98). The functional form of the value function of equity

corresponds to that presented in the R-Model (Proposition 2), but with the vector

be0 =

[−Ae00 − Ae01 S0 + θ0e1l (S0)

e1h(sU0; c

A0 + cB1

)+ d1h

(sU0; c

B1

)− I − Ae00 − Ae01 U0

]. (102)

57

The associated smooth-pasting conditions are:

∂

∂Xe0 (X) |X=S0 = θ

∂

∂Xe1l (X) |X=S0 (103)

∂

∂Xe0 (X) |X=U0 =

∂

∂Xe1h (sX; c1) |X=U0 +

∂

∂Xd1h(sX; cB1

)|X=U0 (104)

Finally, equity holders choose the initial capital structure by maximizing the value of

their objective function ex-ante. Therefore, equity holders solve

cA0 = arg maxcA0

{e0 (X0) + d0 (X0)} . (105)

Equity holders’ problem consists of solving Eq. (105) subject to Eqs. (103)-(104). A

closed-form solution does not exist. We use numerical procedures and verify the optimal-

ity of the investment and reorganization boundaries numerically.

Similar to the valuation of equity, the ODE for the value of debt is given byd0 (X) = (1− θ0) e1l (X) 0 ≤ X ≤ S0

rd0 (X) = cA0 + µXd′0 (X) + 12σ2X2d′′0 (X) S0 < X < U0

d0 (X) = d1h(sX; cA0

)X ≥ U0,

(106)

subject to the boundary conditions

d0 (S0) = (1− θ0) e1l (XS) , d0 (U0) = d1h(sX; cA0

). (107)

In particular, in case of investment, the value of initial debt is still determined by initial

coupon payments cA0 , but incorporates the increase in default risk due to the issuance of

new debt. Hence, the functional form of the value function of debt corresponds to that

presented in the R-Model (Proposition 2), but with the vector

bd =

[−Ad0 + (1− θ0) e1l (S0)

d1h(sU0; c

A0

)− Ad0

]. (108)

58

F. Value functions of firms with first-best investment

and financing decisions

FSI-first-best. The FSI-first-best considers a firm in the FSI model, but with firm value

maximizing investment and financing decisions. Specifically, all value-matching condi-

tions in the valuation of corporate securities correspond to those of a FSI-model firm

(see Appendix E). In the FSI-first-best, however, the smooth-pasting condition at the in-

vestment boundary and the new coupon at investment are firm value-maximizing instead

of equity-value maximizing as in the FSI-model. Specifically, the first-best coupon cfb1

is installed at investment instead of equity holders’ coupon choice determined by condi-

tion (98). Further, we replace the smooth-pasting condition (104) by the condition that

ensures firm value maximization:

∂

∂Xe0 (X) |X=U0 +

∂

∂Xd0 (X) |X=U0 = f1hs. (109)

R-first-best. Recall that the R-model implies first-best financing at investment. The R-

first-best corresponds to a firm in the R-model, but with firm value maximizing investment

decision. Specifically, all value-matching conditions in the valuation of corporate securi-

ties correspond to those of a R-model firm (see Appendix D). In the R-first-best, however,

the smooth-pasting condition at the investment boundary is firm value-maximizing in-

stead of equity-value maximizing as in the R-model. We replace the smooth-pasting

condition (37) by the condition that ensures firm value maximization:

∂

∂Xe0 (X) |X=U0 +

∂

∂Xd0 (X) |X=U0 = f1hs. (110)

G. Waiting time to debt renegotiation

Standard arguments imply that Mt := E [T0 |Ft ] is a martingale, in which T0 corresponds

to the waiting time to covenant renegotiation at investment or initial reorganization

(defined in Eq. (41)). Further:

Mt = E [T01T0≤t + T01T0>t |Ft ] = T01T0≤t + E [(T0 − t) 1T0≤t + t1T0>t |Ft ] (111)

= T01T0≤t + t1T0>t + E [(T0 − t) 1T0>t |Ft ] = T01T0≤t + 1T0>t (t+ w (Xt)) ,

59

in which we used the Markov property, and w (Xt) = E [(T0 − t) |Ft ] denotes the waiting

time to any renegotiation (either distressed or covenant renegotiation) from time t on.

An application of Ito’s lemma shows that for T0 ≤ t, w (X) solves the ODE

µXw′ (X) +1

2σ2X2w′′ (X) + 1 = 0, (112)

subject to the boundary conditions

w (S0) = 0, w (U0) = 0. (113)

The solution is given by

w (X) =2σ2

2µ− σ2− 2 log (X)

2µ− σ2+ 2

(2S

1− 2µ

σ2

0 µ log (U0)− 2U1− 2µ

σ2

0 µ log (S0)

+S2µ

σ2−1

0 σ2 exp

(−1

σ2

(2µ− σ2

)(log (S0) + log (U0))

)−U

2µ

σ2−1

0 σ2 exp

(−1

σ2

(2µ− σ2

)(log (S0) + log (U0))

)(114)

−S1− 2µ

σ2

0 σ2 log (U0) + U1− 2µ

σ2

0 σ2 log (S0)

)((2µ− σ2

)2(S1− 2µ

σ2

0 − U1− 2µ

σ2

0

))−1+ (2 log (U0)− 2 log (U0))

(X

2µ

σ2−1 (2µ− σ2

)S1− 2µ

σ2

0 − U1− 2µ

σ2

0

)−1.

Similarly, Nt := P (T0 = Uν0 |Ft ) is a martingale. Using analogous arguments, the ODE

for the probability of covenant renegotiation, u (Xt) = E[1T0=Uν0 |Ft

], reads

µXu′ (X) +1

2σ2X2u′′ (X) = 0, (115)

subject to the boundary conditions

u (S0) = 0, u (U0) = 1. (116)

The solution is given by

u (X) =1

S2µ

σ2−1

0 − U2µ

σ2−1

0

((X

S0U0

)1− 2µ

σ2

− U2µ

σ2−1

0

). (117)

60